One entry per document, generated from frontmatter — edit the fragments in
this directory, then run luria index.
Quantum foundations (76) — what quantum theory says about the world — contextuality, epistemic restrictions, interference, reconstructions and toy theories, quantum thermodynamics: 010 · 011 · 012 · 014 · 015 · 016 · 017 · 020 · 021 · 024 · 037 · 041 · 042 · 160 · 171 · 174 · 231 · 255 · 309 · 315 · 403 · 416 · 455 · 459 · 474 · 479 · 482 · 485 · 513 · 516 · 524 · 526 · 535 · 545 · 553 · 559 · 580 · 584 · 585 · 586 · 592 · 594 · 605 · 619 · 621 · 630 · 631 · 635 · 656 · 664 · 669 · 687 · 690 · 695 · 720 · 721 · 807 · 1053 · 1055 · 1058 · 1066 · 1068 · 1069 · 1071 · 1074 · 1075 · 1076 · 1078 · 1080 · 1081 · 1091 · 1093 · 1170 · 1213 · 1222 · 1230
Contextuality (33) — whether outcomes can be explained without reference to the context of measurement — Kochen–Specker and Bell contextuality and their sheaf-theoretic form, generalized (Spekkens) contextuality, noncontextual models and their limits, and contextuality outside physics: 010 · 011 · 012 · 013 · 014 · 015 · 016 · 020 · 024 · 037 · 165 · 168 · 171 · 174 · 177 · 231 · 303 · 309 · 315 · 403 · 474 · 516 · 524 · 526 · 553 · 559 · 580 · 619 · 623 · 720 · 722 · 875 · 1170
Mathematics (259) — mathematics read for itself — category theory, topoi and sheaves, spectral geometry, set and measure theory — including mathematical frameworks applied to other fields: 003 · 004 · 005 · 007 · 008 · 009 · 012 · 014 · 016 · 017 · 018 · 019 · 020 · 021 · 022 · 027 · 031 · 032 · 037 · 038 · 041 · 042 · 082 · 084 · 086 · 087 · 106 · 134 · 156 · 157 · 158 · 160 · 165 · 168 · 171 · 174 · 180 · 183 · 184 · 189 · 191 · 192 · 193 · 196 · 206 · 233 · 234 · 236 · 239 · 247 · 254 · 257 · 260 · 276 · 277 · 284 · 288 · 297 · 299 · 301 · 303 · 304 · 312 · 313 · 314 · 323 · 325 · 338 · 340 · 348 · 352 · 357 · 366 · 369 · 370 · 371 · 372 · 373 · 380 · 381 · 388 · 390 · 391 · 392 · 393 · 394 · 395 · 396 · 397 · 398 · 399 · 400 · 401 · 407 · 408 · 420 · 427 · 430 · 437 · 441 · 445 · 456 · 474 · 478 · 479 · 486 · 493 · 498 · 502 · 503 · 509 · 515 · 516 · 519 · 524 · 526 · 530 · 544 · 553 · 559 · 565 · 566 · 568 · 574 · 576 · 584 · 585 · 592 · 595 · 604 · 618 · 619 · 620 · 629 · 642 · 645 · 652 · 654 · 664 · 685 · 686 · 697 · 698 · 713 · 717 · 718 · 719 · 720 · 721 · 722 · 723 · 724 · 726 · 727 · 728 · 729 · 730 · 731 · 733 · 734 · 735 · 736 · 738 · 739 · 740 · 741 · 744 · 745 · 746 · 747 · 749 · 751 · 752 · 753 · 754 · 755 · 757 · 758 · 760 · 761 · 762 · 763 · 770 · 771 · 772 · 773 · 775 · 776 · 811 · 812 · 819 · 820 · 821 · 822 · 829 · 847 · 875 · 894 · 896 · 916 · 924 · 926 · 940 · 944 · 946 · 971 · 981 · 1052 · 1054 · 1056 · 1057 · 1059 · 1060 · 1062 · 1063 · 1064 · 1065 · 1067 · 1070 · 1077 · 1079 · 1082 · 1088 · 1089 · 1090 · 1092 · 1094 · 1096 · 1121 · 1123 · 1128 · 1129 · 1130 · 1132 · 1133 · 1135 · 1136 · 1138 · 1140 · 1141 · 1142 · 1147 · 1149 · 1150 · 1152 · 1155 · 1156 · 1159 · 1160 · 1168 · 1170 · 1177 · 1210 · 1254 · 1256 · 1264 · 1267 · 1303 · 1309
Game theory (52) — strategic interaction and its equilibria — evolutionary stability, repeated games, bargaining, coordination, signalling and conventions — in biology, economics and philosophy (ADR-019): 067 · 149 · 290 · 404 · 414 · 437 · 457 · 466 · 468 · 567 · 672 · 835 · 837 · 844 · 853 · 860 · 894 · 896 · 899 · 924 · 925 · 926 · 928 · 929 · 930 · 931 · 932 · 933 · 934 · 935 · 936 · 938 · 939 · 940 · 941 · 942 · 943 · 944 · 945 · 946 · 947 · 950 · 957 · 961 · 962 · 963 · 964 · 1117 · 1199 · 1231 · 1233 · 1234
Network science (66) — the structure and dynamics of networks — dimension, curvature and Ricci flow, community detection, consensus and synchronization: 058 · 097 · 143 · 146 · 148 · 178 · 188 · 190 · 193 · 242 · 254 · 276 · 321 · 365 · 370 · 385 · 421 · 422 · 456 · 502 · 576 · 598 · 649 · 659 · 660 · 675 · 780 · 799 · 803 · 815 · 825 · 845 · 855 · 887 · 902 · 916 · 960 · 993 · 1008 · 1056 · 1059 · 1062 · 1065 · 1070 · 1082 · 1087 · 1088 · 1090 · 1129 · 1130 · 1132 · 1139 · 1140 · 1141 · 1147 · 1152 · 1156 · 1158 · 1159 · 1160 · 1161 · 1174 · 1210 · 1212 · 1220 · 1232
Complex systems (150) — emergence, information decomposition, individuality, self-organization — how collective behaviour arises from parts: 036 · 058 · 069 · 072 · 073 · 088 · 099 · 128 · 129 · 130 · 132 · 134 · 136 · 144 · 153 · 178 · 179 · 188 · 190 · 193 · 214 · 216 · 217 · 218 · 222 · 223 · 224 · 232 · 257 · 262 · 265 · 268 · 272 · 276 · 285 · 304 · 307 · 323 · 324 · 325 · 402 · 412 · 424 · 459 · 497 · 508 · 532 · 543 · 548 · 571 · 581 · 598 · 607 · 608 · 618 · 634 · 655 · 657 · 661 · 671 · 692 · 696 · 701 · 702 · 703 · 706 · 707 · 708 · 712 · 714 · 715 · 716 · 724 · 727 · 733 · 752 · 755 · 756 · 758 · 762 · 764 · 771 · 773 · 780 · 787 · 795 · 799 · 800 · 803 · 804 · 818 · 819 · 820 · 822 · 831 · 863 · 885 · 891 · 899 · 905 · 927 · 928 · 936 · 939 · 942 · 945 · 1052 · 1054 · 1061 · 1073 · 1079 · 1085 · 1087 · 1095 · 1097 · 1122 · 1126 · 1161 · 1162 · 1167 · 1179 · 1181 · 1183 · 1209 · 1218 · 1227 · 1231 · 1232 · 1233 · 1248 · 1250 · 1251 · 1266 · 1267 · 1271 · 1273 · 1292 · 1301 · 1302 · 1306 · 1309 · 1314 · 1315 · 1321 · 1323 · 1333 · 1335 · 1340 · 1343 · 1348
Probabilistic modeling (104) — Bayesian inference and statistical models outside deep learning — nonparametric priors, topic models, samplers: 028 · 031 · 066 · 068 · 073 · 079 · 081 · 087 · 155 · 157 · 158 · 166 · 172 · 177 · 199 · 203 · 215 · 247 · 256 · 280 · 289 · 305 · 306 · 313 · 336 · 339 · 349 · 354 · 366 · 378 · 405 · 419 · 426 · 455 · 472 · 475 · 489 · 515 · 534 · 542 · 545 · 550 · 562 · 564 · 569 · 587 · 611 · 614 · 617 · 696 · 718 · 744 · 762 · 769 · 775 · 785 · 796 · 805 · 808 · 811 · 816 · 818 · 819 · 829 · 882 · 883 · 923 · 937 · 951 · 952 · 954 · 956 · 958 · 960 · 969 · 972 · 985 · 989 · 993 · 999 · 1003 · 1006 · 1008 · 1010 · 1012 · 1015 · 1019 · 1034 · 1037 · 1041 · 1043 · 1044 · 1045 · 1046 · 1097 · 1191 · 1242 · 1245 · 1253 · 1255 · 1257 · 1258 · 1296 · 1304
Neuroscience (84) — brains and nervous systems — representation, coding and dynamics measured in biological tissue: 045 · 059 · 062 · 063 · 070 · 088 · 090 · 093 · 094 · 096 · 097 · 098 · 100 · 102 · 103 · 124 · 191 · 192 · 240 · 245 · 252 · 261 · 262 · 272 · 285 · 291 · 296 · 298 · 300 · 302 · 322 · 336 · 410 · 454 · 484 · 500 · 529 · 571 · 593 · 603 · 618 · 660 · 682 · 697 · 765 · 766 · 767 · 768 · 769 · 800 · 827 · 830 · 870 · 871 · 873 · 878 · 880 · 881 · 883 · 886 · 893 · 895 · 909 · 923 · 1110 · 1178 · 1179 · 1191 · 1196 · 1237 · 1241 · 1242 · 1299 · 1301 · 1302 · 1312 · 1314 · 1317 · 1326 · 1329 · 1337 · 1340 · 1341 · 1346
Natural sciences (95) — physics, astronomy, planetary and earth science, chemistry, biology and medicine read outside any machine-learning claim: 026 · 030 · 072 · 099 · 128 · 129 · 130 · 135 · 160 · 178 · 179 · 191 · 194 · 197 · 198 · 202 · 205 · 275 · 304 · 323 · 325 · 408 · 431 · 463 · 466 · 473 · 499 · 508 · 517 · 543 · 562 · 567 · 634 · 655 · 660 · 663 · 672 · 679 · 682 · 742 · 747 · 748 · 749 · 750 · 752 · 754 · 760 · 763 · 772 · 774 · 776 · 777 · 780 · 789 · 817 · 818 · 821 · 1008 · 1049 · 1085 · 1095 · 1098 · 1099 · 1100 · 1101 · 1102 · 1103 · 1104 · 1105 · 1106 · 1107 · 1108 · 1109 · 1195 · 1197 · 1200 · 1201 · 1203 · 1205 · 1206 · 1208 · 1209 · 1211 · 1214 · 1215 · 1219 · 1223 · 1228 · 1265 · 1268 · 1270 · 1273 · 1315 · 1323 · 1343
Ecology (12) — how organisms interact with each other and their environment — symbiosis and host–microbe partnerships, competition, herbivory and trophic interactions, community structure, resilience and regime shifts in ecosystems (ADR-028). How a partner comes to live inside another and depend on it is endosymbiosis (ADR-055): 128 · 130 · 132 · 136 · 469 · 473 · 548 · 560 · 1048 · 1162 · 1168 · 1235
Endosymbiosis and reductive evolution (31) — how one organism comes to live inside another and depend on it, and how that ends — reductive genome evolution by drift, deletional bias or adaptive loss (including the Black Queen dependencies of free-living microbes), complementary loss across partners, nested symbioses and symbiont splitting and replacement, endosymbiotic gene transfer, protein import and host control of transmission, organellogenesis and organelle loss, and eukaryogenesis. The ecology of a partnership is ecology (ADR-055): 1048 · 1049 · 1050 · 1051 · 1098 · 1099 · 1100 · 1101 · 1102 · 1103 · 1104 · 1105 · 1106 · 1107 · 1108 · 1109 · 1197 · 1200 · 1201 · 1203 · 1205 · 1206 · 1208 · 1211 · 1214 · 1215 · 1219 · 1223 · 1228 · 1235 · 1243
Thermodynamics (34) — the second law and its extensions read for themselves — entropy and entropy production, irreversibility, nonequilibrium steady states and their stability, dissipative structures, fluctuation theorems and stochastic thermodynamics, and the thermodynamics of computation and of life (ADR-020): 026 · 030 · 072 · 209 · 211 · 220 · 275 · 412 · 416 · 431 · 463 · 482 · 492 · 513 · 517 · 532 · 671 · 676 · 679 · 692 · 779 · 790 · 817 · 831 · 1248 · 1250 · 1253 · 1261 · 1264 · 1265 · 1266 · 1268 · 1270 · 1273
Operations research (15) — optimization of real systems — routing, scheduling, facility location, combinatorial algorithms: 332 · 345 · 350 · 356 · 364 · 375 · 377 · 378 · 382 · 383 · 386 · 501 · 654 · 668 · 1303
Society and governance (80) — law, politics, policy, security and institutions — court records, doctrine, democratic theory, information operations: 025 · 027 · 127 · 137 · 140 · 144 · 149 · 150 · 152 · 153 · 173 · 207 · 218 · 219 · 223 · 235 · 317 · 326 · 327 · 329 · 411 · 423 · 428 · 429 · 434 · 435 · 440 · 450 · 470 · 480 · 483 · 488 · 533 · 551 · 555 · 561 · 615 · 627 · 637 · 639 · 651 · 659 · 725 · 833 · 836 · 837 · 838 · 841 · 842 · 850 · 851 · 852 · 854 · 856 · 857 · 858 · 859 · 860 · 862 · 885 · 889 · 898 · 906 · 911 · 919 · 1062 · 1088 · 1165 · 1173 · 1181 · 1198 · 1202 · 1207 · 1217 · 1221 · 1225 · 1229 · 1238 · 1283 · 1352
Information theory (132) — entropy, channels, coding and capacity read for themselves — including information-theoretic accounts of work, memory and inference outside machine learning: 001 · 005 · 006 · 026 · 028 · 030 · 031 · 035 · 036 · 039 · 083 · 156 · 161 · 163 · 194 · 198 · 204 · 205 · 222 · 227 · 237 · 238 · 240 · 244 · 248 · 257 · 259 · 260 · 262 · 263 · 266 · 268 · 270 · 275 · 277 · 281 · 293 · 308 · 313 · 352 · 357 · 399 · 404 · 416 · 424 · 426 · 479 · 497 · 513 · 523 · 529 · 568 · 581 · 584 · 599 · 602 · 617 · 641 · 668 · 676 · 695 · 700 · 701 · 702 · 705 · 706 · 707 · 708 · 709 · 710 · 711 · 712 · 713 · 714 · 715 · 716 · 717 · 719 · 733 · 742 · 743 · 748 · 750 · 751 · 753 · 756 · 757 · 764 · 784 · 787 · 788 · 789 · 791 · 804 · 806 · 809 · 811 · 817 · 820 · 822 · 840 · 844 · 846 · 853 · 881 · 884 · 1025 · 1053 · 1055 · 1056 · 1058 · 1060 · 1066 · 1067 · 1069 · 1077 · 1092 · 1093 · 1096 · 1125 · 1127 · 1143 · 1146 · 1163 · 1167 · 1169 · 1177 · 1245 · 1254 · 1259 · 1336 · 1344
Representation learning (208) — how learned systems come to represent their data — self-supervised and contrastive objectives, spectral embeddings, information bottlenecks, knowledge-graph embeddings, and whether representations converge: 001 · 002 · 003 · 004 · 005 · 006 · 007 · 008 · 009 · 017 · 018 · 019 · 021 · 022 · 035 · 039 · 078 · 083 · 086 · 104 · 111 · 113 · 116 · 117 · 169 · 175 · 176 · 181 · 182 · 183 · 185 · 186 · 189 · 194 · 195 · 196 · 197 · 200 · 201 · 202 · 212 · 227 · 228 · 229 · 230 · 233 · 234 · 236 · 237 · 238 · 239 · 241 · 243 · 246 · 251 · 256 · 264 · 269 · 271 · 274 · 278 · 279 · 281 · 282 · 283 · 284 · 286 · 287 · 288 · 292 · 294 · 299 · 301 · 305 · 306 · 312 · 319 · 320 · 420 · 421 · 439 · 445 · 478 · 481 · 496 · 503 · 504 · 565 · 566 · 640 · 683 · 698 · 719 · 723 · 728 · 730 · 732 · 734 · 737 · 738 · 739 · 740 · 745 · 746 · 759 · 775 · 782 · 786 · 788 · 789 · 793 · 794 · 797 · 798 · 802 · 805 · 808 · 813 · 825 · 865 · 869 · 965 · 966 · 967 · 968 · 970 · 971 · 973 · 974 · 975 · 976 · 977 · 978 · 979 · 980 · 982 · 983 · 984 · 986 · 987 · 988 · 990 · 991 · 992 · 994 · 995 · 996 · 997 · 998 · 1000 · 1001 · 1002 · 1004 · 1005 · 1007 · 1011 · 1013 · 1014 · 1016 · 1017 · 1018 · 1020 · 1021 · 1022 · 1023 · 1024 · 1026 · 1027 · 1028 · 1029 · 1030 · 1031 · 1032 · 1033 · 1035 · 1036 · 1038 · 1039 · 1040 · 1042 · 1045 · 1047 · 1124 · 1127 · 1128 · 1133 · 1135 · 1136 · 1139 · 1141 · 1143 · 1145 · 1149 · 1155 · 1185 · 1187 · 1220 · 1224 · 1226 · 1262 · 1263 · 1274 · 1313 · 1330 · 1334 · 1339 · 1342 · 1350
Learning theory (151) — why learning generalizes and how it proceeds — compression and description length, Kolmogorov complexity and sufficient statistics, rate–distortion and PAC-style bounds, model selection; and training dynamics: solvable models of learning trajectories, stages, plateaus and phase transitions in training, and the implicit bias of optimisation. A work whose subject is how to train a model better is ML practice and goes to the anthology (ADR-036): 022 · 026 · 028 · 030 · 033 · 035 · 039 · 078 · 079 · 080 · 082 · 083 · 084 · 085 · 086 · 087 · 104 · 106 · 108 · 117 · 169 · 180 · 181 · 182 · 186 · 187 · 195 · 200 · 201 · 204 · 206 · 209 · 210 · 211 · 212 · 213 · 228 · 229 · 238 · 239 · 241 · 244 · 246 · 248 · 253 · 259 · 263 · 266 · 270 · 274 · 277 · 278 · 279 · 283 · 286 · 289 · 293 · 294 · 314 · 318 · 319 · 320 · 331 · 342 · 349 · 354 · 359 · 439 · 481 · 510 · 521 · 574 · 614 · 726 · 735 · 737 · 738 · 739 · 740 · 759 · 761 · 778 · 779 · 781 · 782 · 783 · 784 · 786 · 788 · 790 · 792 · 793 · 794 · 797 · 806 · 809 · 813 · 839 · 840 · 846 · 861 · 899 · 905 · 925 · 927 · 928 · 929 · 930 · 931 · 932 · 933 · 936 · 937 · 941 · 945 · 947 · 950 · 957 · 961 · 962 · 963 · 964 · 967 · 973 · 975 · 981 · 990 · 997 · 1001 · 1009 · 1057 · 1199 · 1218 · 1231 · 1234 · 1249 · 1252 · 1253 · 1254 · 1255 · 1256 · 1257 · 1258 · 1259 · 1260 · 1262 · 1263 · 1269 · 1272 · 1274 · 1275
Compositionality (34) — how the structure and meaning of a whole come from its parts and how they are combined — the principle of compositionality and compositional semantics, the emergence of compositional structure in languages under transmission, and composition and binding in learned models (generalization to unseen combinations, attribute binding, composing distributions or concepts). A work on making a model generalize compositionally is ML practice and goes to the anthology (ADR-031): 117 · 164 · 167 · 185 · 195 · 199 · 200 · 201 · 203 · 250 · 405 · 519 · 522 · 611 · 678 · 686 · 778 · 786 · 794 · 948 · 949 · 955 · 958 · 977 · 988 · 1054 · 1057 · 1063 · 1089 · 1140 · 1154 · 1158 · 1164 · 1171
Mathematical statistics (43) — the theory of statistical inference read for itself — comparison and sufficiency of experiments (Blackwell, Le Cam deficiency), statistical decision theory, the sufficiency theorems (Fisher–Neyman, Basu, Bahadur) and bounds on estimation. Bayesian modelling is probabilistic-modeling (ADR-031): 156 · 157 · 161 · 176 · 215 · 280 · 308 · 318 · 391 · 534 · 641 · 704 · 705 · 709 · 717 · 743 · 778 · 812 · 894 · 951 · 952 · 954 · 956 · 972 · 985 · 993 · 999 · 1006 · 1010 · 1012 · 1015 · 1019 · 1034 · 1037 · 1041 · 1043 · 1044 · 1046 · 1096 · 1177 · 1269 · 1312 · 1337
Information retrieval (22) — finding what is relevant to a need — document and query representation, relevance and aboutness, ranking and feedback, and the geometric, probabilistic and logical models of retrieval: 017 · 261 · 361 · 363 · 365 · 366 · 368 · 369 · 370 · 372 · 376 · 379 · 384 · 385 · 388 · 480 · 697 · 815 · 832 · 969 · 989 · 1003
Databases and data structures (40) — how stored data is organized so that it can be found and kept current — physical database design and index selection, materialized views and the choice of which answers to precompute, adaptive and self-organizing structures, lower bounds on lookup, caching and paging; and the cost of organizing ahead of use against organizing in use. Read for itself, not as ML practice: learned indexes and other machine-learning approaches go to the anthology (ADR-045): 332 · 333 · 338 · 340 · 341 · 344 · 345 · 348 · 350 · 356 · 361 · 362 · 363 · 364 · 365 · 367 · 368 · 369 · 371 · 372 · 373 · 374 · 375 · 376 · 377 · 378 · 379 · 380 · 381 · 382 · 383 · 384 · 385 · 386 · 387 · 388 · 389 · 815 · 832 · 1244
Design rationale (1) — recording the reasoning behind a design or decision as it is made — issues, positions and arguments, options and criteria (IBIS, gIBIS, QOC and their successors) — and why such capture systems are or are not used: who bears the cost of capture and who gets the benefit, premature formalization, cognitive overhead, and the groupware adoption problems behind them (ADR-030): 311
Social science (112) — economics, psychology, anthropology and sociology — empirical and theoretical work on people and societies that is not law or policy: 013 · 025 · 046 · 047 · 049 · 052 · 060 · 074 · 077 · 123 · 126 · 140 · 142 · 144 · 145 · 149 · 152 · 153 · 154 · 164 · 166 · 167 · 173 · 214 · 216 · 218 · 224 · 242 · 267 · 290 · 295 · 311 · 321 · 329 · 335 · 337 · 406 · 414 · 429 · 432 · 450 · 483 · 494 · 537 · 539 · 552 · 555 · 572 · 597 · 601 · 608 · 615 · 648 · 653 · 674 · 693 · 795 · 796 · 810 · 814 · 824 · 826 · 833 · 834 · 835 · 836 · 837 · 838 · 841 · 842 · 850 · 851 · 852 · 854 · 856 · 858 · 859 · 860 · 862 · 863 · 887 · 889 · 890 · 891 · 902 · 916 · 918 · 919 · 935 · 960 · 1061 · 1073 · 1111 · 1112 · 1113 · 1114 · 1115 · 1116 · 1164 · 1171 · 1181 · 1183 · 1192 · 1212 · 1217 · 1221 · 1225 · 1279 · 1281 · 1284 · 1308 · 1325
Causality (84) — causation and the structure of causal relations — causal order, definite and indefinite, and its combinatorics, topology and geometry; sheaf- and process-theoretic accounts of causality; causal models, causal inference and interventionist accounts of what a causal relation is; and the metaphysics of causation — exclusion, mental causation, causal emergence and closure, reciprocal causation (ADR-035): 058 · 133 · 138 · 171 · 177 · 222 · 231 · 243 · 275 · 282 · 287 · 410 · 419 · 424 · 446 · 451 · 485 · 491 · 497 · 527 · 580 · 612 · 674 · 700 · 701 · 703 · 704 · 707 · 710 · 711 · 764 · 787 · 801 · 802 · 820 · 824 · 839 · 843 · 847 · 848 · 849 · 861 · 889 · 965 · 966 · 968 · 970 · 974 · 978 · 979 · 980 · 983 · 987 · 994 · 995 · 996 · 998 · 1000 · 1002 · 1007 · 1011 · 1014 · 1020 · 1021 · 1023 · 1024 · 1025 · 1026 · 1029 · 1031 · 1039 · 1061 · 1123 · 1125 · 1137 · 1146 · 1167 · 1169 · 1225 · 1287 · 1288 · 1291 · 1293 · 1294
Pragmatics (19) — language in use — speech acts and illocutionary force, assertion and common ground, presupposition, dynamic and update semantics, footing and stance in discourse, and probabilistic models of speakers and listeners (rational speech acts); what an utterance does, beyond what it says (ADR-034): 162 · 172 · 226 · 264 · 406 · 444 · 472 · 511 · 623 · 665 · 693 · 785 · 816 · 1120 · 1131 · 1144 · 1148 · 1153 · 1157
Myth and folklore (3) — myths, folktales and their variants as objects of study — morphology of the folktale, structural and transformational analysis of myth, and the computational modelling of either (ADR-034): 167 · 432 · 1164
Translation (11) — translation and its theory — equivalence and its kinds (formal, dynamic, functional), interpretive resemblance, register and quality assessment, translation as skopos-driven action, intersemiotic translation between media, and what a translation preserves or changes (ADR-033): 170 · 226 · 270 · 806 · 1120 · 1134 · 1142 · 1143 · 1145 · 1151 · 1153
Linguistics (25) — the study of language itself — morphology, lexicalism, word segmentation, syntax and semantics as linguists pose them, not as models encode them: 017 · 155 · 159 · 162 · 163 · 164 · 170 · 172 · 204 · 271 · 477 · 518 · 542 · 588 · 623 · 643 · 670 · 693 · 784 · 785 · 791 · 1004 · 1131 · 1144 · 1171
Metaphysics (88) — what exists and what it is to exist — causation, emergence and levels, laws, time — as a philosophical question (group: philosophy): 029 · 032 · 034 · 036 · 038 · 040 · 043 · 048 · 058 · 064 · 065 · 092 · 095 · 119 · 127 · 133 · 138 · 252 · 273 · 316 · 328 · 415 · 417 · 436 · 441 · 447 · 448 · 452 · 453 · 471 · 476 · 485 · 487 · 506 · 507 · 531 · 535 · 538 · 540 · 546 · 556 · 563 · 575 · 579 · 589 · 594 · 609 · 610 · 612 · 621 · 622 · 625 · 630 · 631 · 633 · 635 · 638 · 644 · 646 · 650 · 656 · 669 · 670 · 681 · 687 · 690 · 691 · 694 · 867 · 868 · 872 · 877 · 1068 · 1071 · 1080 · 1081 · 1083 · 1086 · 1091 · 1118 · 1194 · 1222 · 1230 · 1276 · 1282 · 1286 · 1314 · 1333
Mereology (26) — parts and wholes — composition, individuation of systems and collectives (group: philosophy): 017 · 043 · 232 · 443 · 448 · 452 · 476 · 493 · 507 · 512 · 514 · 528 · 540 · 549 · 582 · 583 · 585 · 589 · 591 · 622 · 644 · 1287 · 1288 · 1291 · 1293 · 1294
Agency (80) — what it is to be an agent — goals, action, control and the capacity to act — in organisms, collectives or machines. An agent is not thereby an individual, a self or a person (ADR-024); how an agent’s behaviour is integrated is behavioral-integration, and governing oneself by one’s own standards is self-governance (group: philosophy): 026 · 029 · 040 · 043 · 047 · 049 · 054 · 055 · 056 · 061 · 065 · 067 · 071 · 075 · 076 · 118 · 119 · 120 · 121 · 122 · 127 · 131 · 139 · 173 · 207 · 208 · 219 · 220 · 225 · 232 · 235 · 249 · 258 · 265 · 300 · 322 · 328 · 458 · 460 · 461 · 495 · 527 · 536 · 538 · 583 · 596 · 606 · 616 · 624 · 628 · 636 · 658 · 689 · 699 · 801 · 817 · 890 · 976 · 1027 · 1032 · 1117 · 1118 · 1119 · 1165 · 1166 · 1236 · 1249 · 1260 · 1280 · 1285 · 1296 · 1297 · 1300 · 1321 · 1335 · 1336 · 1340 · 1341 · 1344 · 1348
Individuation (53) — what makes something one thing, and the same thing over time or across descriptions — individuation, numerical identity and diversity, individuality and persistence of things of any kind, biological individuality and organisational closure. Selves are self and persons are personhood (group: philosophy; ADR-015, ADR-024): 032 · 034 · 066 · 071 · 072 · 073 · 135 · 141 · 221 · 249 · 254 · 265 · 268 · 413 · 417 · 418 · 424 · 443 · 447 · 448 · 452 · 453 · 465 · 476 · 490 · 514 · 531 · 535 · 546 · 549 · 575 · 579 · 583 · 607 · 622 · 650 · 666 · 1050 · 1051 · 1097 · 1107 · 1119 · 1163 · 1194 · 1211 · 1243 · 1247 · 1276 · 1277 · 1278 · 1280 · 1285 · 1351
Self (35) — what a self is — the minimal, bodily and pre-reflective self, self-models and the sense of being a subject, the self as process or as context, and whether machines or groups can be selves. Not the person, which is personhood (group: philosophy; ADR-024): 044 · 051 · 054 · 063 · 064 · 074 · 093 · 147 · 406 · 409 · 458 · 490 · 590 · 650 · 681 · 684 · 691 · 765 · 766 · 767 · 768 · 769 · 827 · 872 · 1114 · 1115 · 1295 · 1298 · 1299 · 1300 · 1313 · 1330 · 1334 · 1339 · 1350
Personhood (15) — what a person is and what makes one persist — personal identity over time, psychological continuity and what matters in survival, persons as bearers of reasons, rights and responsibility. Not the self, which is self (group: philosophy; ADR-024): 060 · 065 · 075 · 076 · 120 · 131 · 417 · 447 · 464 · 476 · 531 · 546 · 590 · 650 · 681
Behavioral integration (28) — how an organism’s many control systems come to act as one — action selection and competition between systems (habitual and goal-directed, automatic and willed), hierarchical and feedback control, intertemporal conflict and self-control, and evidence accumulation to a decision. One of four unities kept apart (ADR-024): 056 · 059 · 061 · 062 · 067 · 068 · 069 · 070 · 076 · 101 · 302 · 307 · 324 · 409 · 484 · 680 · 688 · 689 · 904 · 908 · 913 · 918 · 1110 · 1117 · 1175 · 1176 · 1192 · 1227
Phenomenal unity (5) — the unity of experience — what makes simultaneous experiences one subject’s, and how a self-model or a perspective binds them. One of four unities kept apart (group: philosophy; ADR-024): 063 · 573 · 644 · 875 · 882
Narrative unity (6) — the unity a life has as a story — narrative identity, the narrative self, autobiographical reasoning, and the claim and counter-claim that a self is the story told of it. One of four unities kept apart (group: philosophy; ADR-024): 044 · 060 · 076 · 525 · 684 · 691
Self-governance (20) — governing oneself by standards that are one’s own — identification and wholeheartedness, planning agency and policies, self-constitution, autonomy and authenticity, and the empirical psychology of self-endorsed motives. One of four unities kept apart (group: philosophy; ADR-024): 029 · 040 · 047 · 049 · 054 · 065 · 074 · 075 · 076 · 077 · 120 · 121 · 122 · 219 · 590 · 904 · 1118 · 1165 · 1176 · 1331
Phenomenology (16) — the first-person description of experience as a method — the philosophical tradition (Husserl, Heidegger, Merleau-Ponty), its use in the sciences of mind, and the theories that take their data from it (group: philosophy; ADR-016): 044 · 064 · 458 · 498 · 597 · 768 · 866 · 867 · 868 · 870 · 880 · 959 · 1241 · 1246 · 1295 · 1299
Social ontology (34) — what social facts, groups, institutions and social kinds are, and what makes them exist — collective intentionality, joint commitment, status functions, convention, social construction, and whether groups can be agents or minds (group: philosophy; ADR-017): 057 · 065 · 125 · 126 · 127 · 131 · 137 · 139 · 351 · 414 · 418 · 429 · 487 · 511 · 520 · 536 · 549 · 575 · 625 · 626 · 648 · 667 · 725 · 1083 · 1086 · 1112 · 1115 · 1247 · 1277 · 1278 · 1279 · 1280 · 1284 · 1285
Social identity (7) — the psychology of group membership — social identity and self-categorization theory, how people categorize themselves and others and when a group identity becomes salient, identification and its measurement, in-group bias and intergroup relations, rivalry, recategorization and common in-group identity, group-based emotion, crowds and fandom. What a group is, as ontology, is social-ontology; here it is how people come to see themselves and act as members (ADR-062): 1111 · 1112 · 1113 · 1114 · 1115 · 1116 · 1352
Altruism and self-interest (2) — whether and how action can aim at another’s good rather than one’s own — psychological egoism and its rivals, the empathy–altruism debate and self–other merging, inclusion of others in the self and identity fusion, team reasoning and group-directed preferences, identity in the utility function, the evolution of unselfish behaviour (kin, reciprocal and group selection), and the extent of the self as it bears on what counts as self-interest (ADR-062): 655 · 1351
Future generations (0) — what the living owe, and why they care about, people who will live after them — longtermism and existential risk, intergenerational justice, the non-identity problem and person-affecting views, population ethics, discounting of future welfare, and the psychology of concern for the future: legacy motivation, generativity, symbolic immortality and continuity with one’s future self (ADR-063).
Moral psychology (18) — morality as a natural phenomenon — moral judgement, emotion and norms, and their evolution, development and variation across cultures; descriptive, where ethics is normative (group: philosophy; ADR-018): 121 · 122 · 147 · 435 · 457 · 468 · 494 · 495 · 505 · 539 · 558 · 613 · 626 · 632 · 653 · 663 · 892 · 1352
Psychopathology and treatment (36) — what a mental disorder is and how psychological treatment changes it — medical models of illness (biomedical, biopsychosocial, network), the philosophy of psychiatry, functional and transdiagnostic accounts of psychopathology such as experiential avoidance and psychological flexibility, and psychotherapies and their mechanisms of change (ADR-021): 044 · 048 · 050 · 051 · 052 · 053 · 058 · 285 · 409 · 560 · 680 · 892 · 895 · 897 · 901 · 903 · 907 · 910 · 912 · 914 · 915 · 917 · 920 · 921 · 922 · 1179 · 1180 · 1182 · 1184 · 1186 · 1189 · 1190 · 1193 · 1320 · 1322 · 1349
Motivation (39) — why organisms act and persist — intrinsic and extrinsic motivation, needs, goals and values, the internalization of regulation, and the difference between autonomous and controlled motives; the empirical counterpart of the philosophy of autonomy under agency (ADR-023):
046 · 047 · 049 · 052 · 054 · 067 · 070 · 077 · 154 · 893 · 895 · 904 · 908 · 913 · 918 · 1110 · 1117 · 1175 · 1176 · 1192 · 1305 · 1307 · 1308 · 1310 · 1311 · 1316 · 1318 · 1319 · 1320 · 1322 · 1324 · 1325 · 1326 · 1327 · 1331 · 1338 · 1345 · 1347 · 1349
Well-being (13) — how well a life goes for the one living it, as psychology measures it — subjective and eudaimonic well-being, flourishing, vitality and meaning in life, and what predicts them (ADR-025): 060 · 074 · 077 · 1305 · 1307 · 1308 · 1310 · 1319 · 1325 · 1327 · 1338 · 1345 · 1347
Learning and conditioning (38) — how organisms learn from contingencies and consequences — Pavlovian and instrumental conditioning, reinforcement and reward learning in brains, habit and goal-directed control, behaviour analysis and relational responding. Not machine learning, which is learning-theory or the anthology (ADR-025): 044 · 046 · 049 · 050 · 062 · 154 · 307 · 324 · 484 · 489 · 688 · 895 · 897 · 900 · 901 · 907 · 909 · 910 · 912 · 914 · 915 · 917 · 920 · 921 · 922 · 923 · 934 · 938 · 1178 · 1180 · 1182 · 1184 · 1186 · 1189 · 1190 · 1191 · 1193 · 1324
Psychometrics (17) — measuring minds — scales, reliability and validity, latent-variable and network models of psychological constructs, and model-based estimation of cognitive parameters (ADR-025): 058 · 061 · 074 · 475 · 505 · 613 · 766 · 892 · 1148 · 1157 · 1311 · 1316 · 1318 · 1327 · 1331 · 1338 · 1347
Philosophy of biology (40) — what life, organisms and biological functions are — teleology and function, organisation and closure, biological individuality and autonomy, and the demarcation of the living (group: philosophy; ADR-025): 071 · 072 · 073 · 135 · 141 · 217 · 220 · 221 · 232 · 413 · 418 · 443 · 446 · 448 · 465 · 469 · 473 · 492 · 514 · 532 · 583 · 607 · 612 · 628 · 658 · 666 · 673 · 770 · 874 · 1097 · 1119 · 1122 · 1126 · 1166 · 1247 · 1251 · 1271 · 1289 · 1292 · 1351
Embodied cognition (31) — cognition as embodied, embedded, enacted or extended — enactivism and sense-making, coordination dynamics, situated robotics, and mind as organism–environment coupling (group: philosophy; ADR-025): 069 · 071 · 221 · 302 · 334 · 343 · 346 · 351 · 355 · 360 · 461 · 512 · 520 · 528 · 579 · 582 · 591 · 628 · 666 · 765 · 766 · 767 · 823 · 827 · 874 · 876 · 891 · 1119 · 1166 · 1194 · 1227
Free will (24) — free will and volition, as philosophy and as science — compatibilism and its rivals, manipulation and responsibility, and the neuroscience of voluntary action such as the readiness potential (group: philosophy; ADR-025): 029 · 040 · 059 · 065 · 067 · 118 · 119 · 120 · 121 · 122 · 139 · 147 · 310 · 316 · 328 · 1118 · 1298 · 1302 · 1321 · 1328 · 1329 · 1332 · 1341 · 1348
Model comparison (11) — choosing between models by their evidence — the marginal likelihood and Bayes factors, the Savage–Dickey density ratio for nested models, Occam factors and the evidence framework, Bayesian model reduction and structure learning, and information criteria and free energies for singular models (ADR-026): 079 · 080 · 081 · 087 · 259 · 564 · 624 · 718 · 1236 · 1253 · 1275
Information geometry (14) — the geometry of statistical models — the Fisher information as a metric, natural gradient, curvature and its Kronecker and block structure, and the spectra of Fisher and Hessian matrices in learned models (ADR-026): 078 · 080 · 082 · 084 · 085 · 087 · 115 · 230 · 427 · 578 · 731 · 742 · 774 · 777
Loss landscapes (39) — the geometry of trained solutions in weight space — mode connectivity, linear and along curves, barriers between minima and the permutation symmetries that hide or remove them, re-basin alignment, star domains and connecting simplexes, local versus global landscape structure, and model merging as its use (ADR-027): 105 · 107 · 108 · 109 · 110 · 111 · 112 · 113 · 114 · 115 · 116 · 184 · 209 · 210 · 211 · 213 · 278 · 286 · 425 · 509 · 521 · 557 · 578 · 675 · 732 · 736 · 741 · 779 · 781 · 790 · 797 · 828 · 975 · 1172 · 1185 · 1187 · 1188 · 1272 · 1275
Control theory (6) — the analysis and design of feedback — stability and Lyapunov certificates, invariance, viability and barrier certificates, input-to-state stability and small-gain conditions, contraction, adaptive, dual and safe control, and controller synthesis under constraints; dynamical systems without a control input stay with complex-systems (ADR-066): 134 · 771 · 773 · 1254 · 1256 · 1267
Ethics (40) — moral philosophy — what is owed, permitted or good — including applied ethics of technology and institutions (group: philosophy): 025 · 027 · 029 · 040 · 075 · 118 · 119 · 120 · 121 · 122 · 207 · 225 · 235 · 258 · 300 · 310 · 316 · 317 · 326 · 327 · 328 · 411 · 428 · 434 · 442 · 449 · 464 · 467 · 525 · 540 · 554 · 561 · 600 · 627 · 667 · 677 · 684 · 699 · 864 · 1173
Consciousness (75) — experience and its theories — phenomenal consciousness, its measures and its attribution to animals or machines (group: philosophy): 023 · 043 · 045 · 059 · 063 · 064 · 090 · 091 · 093 · 094 · 095 · 096 · 098 · 100 · 101 · 102 · 103 · 125 · 240 · 245 · 252 · 296 · 298 · 322 · 415 · 433 · 436 · 449 · 454 · 460 · 461 · 498 · 506 · 507 · 512 · 523 · 554 · 563 · 573 · 577 · 597 · 603 · 606 · 633 · 644 · 662 · 677 · 694 · 699 · 768 · 830 · 865 · 866 · 867 · 868 · 869 · 870 · 873 · 875 · 876 · 879 · 880 · 881 · 882 · 883 · 953 · 959 · 1204 · 1224 · 1226 · 1241 · 1246 · 1295 · 1297 · 1299
Cognition (145) — the mind as information processing — perception, memory, reasoning and cognitive strategies — as studied by cognitive science and philosophy of mind (group: philosophy): 013 · 023 · 031 · 043 · 044 · 048 · 050 · 055 · 056 · 057 · 061 · 063 · 064 · 068 · 070 · 088 · 089 · 091 · 092 · 094 · 095 · 096 · 097 · 098 · 100 · 102 · 103 · 124 · 125 · 137 · 155 · 163 · 166 · 172 · 208 · 220 · 245 · 255 · 261 · 272 · 330 · 334 · 335 · 336 · 337 · 339 · 343 · 346 · 351 · 355 · 358 · 359 · 360 · 402 · 433 · 436 · 438 · 454 · 458 · 460 · 461 · 462 · 471 · 472 · 475 · 489 · 500 · 512 · 520 · 528 · 529 · 538 · 541 · 542 · 545 · 547 · 558 · 563 · 564 · 570 · 573 · 577 · 579 · 582 · 588 · 591 · 593 · 596 · 601 · 603 · 608 · 609 · 616 · 636 · 638 · 646 · 662 · 688 · 785 · 791 · 796 · 800 · 807 · 816 · 823 · 830 · 865 · 869 · 872 · 873 · 874 · 877 · 878 · 879 · 886 · 888 · 900 · 908 · 913 · 959 · 982 · 984 · 1017 · 1018 · 1072 · 1084 · 1110 · 1112 · 1124 · 1154 · 1175 · 1194 · 1196 · 1216 · 1224 · 1226 · 1239 · 1240 · 1242 · 1290 · 1296 · 1297 · 1298 · 1300 · 1317
Emotion and affect (35) — emotions, feelings and affect — what they are, their bodily and neural basis (including the homeostatic and interoceptive states feelings are said to report), their role in decision, memory and behaviour, and whether they ground consciousness (group: philosophy; ADR-014): 045 · 050 · 055 · 056 · 057 · 090 · 093 · 101 · 123 · 125 · 126 · 291 · 329 · 500 · 560 · 570 · 603 · 662 · 663 · 680 · 826 · 871 · 878 · 893 · 898 · 907 · 917 · 1180 · 1186 · 1202 · 1221 · 1237 · 1282 · 1283 · 1286
Philosophy of science (100) — what science is and what its theories say about the world — realism and structural realism, explanation, causation and evidence, the interpretation of physical theories (group: philosophy): 002 · 010 · 023 · 024 · 030 · 034 · 036 · 038 · 048 · 053 · 057 · 058 · 066 · 073 · 091 · 094 · 125 · 133 · 138 · 141 · 143 · 146 · 148 · 151 · 243 · 249 · 273 · 295 · 298 · 410 · 413 · 419 · 422 · 423 · 438 · 441 · 442 · 446 · 451 · 453 · 459 · 463 · 465 · 469 · 485 · 491 · 528 · 537 · 541 · 550 · 556 · 569 · 572 · 586 · 591 · 594 · 600 · 604 · 610 · 612 · 627 · 631 · 637 · 639 · 640 · 648 · 657 · 658 · 669 · 673 · 674 · 687 · 690 · 694 · 802 · 814 · 824 · 855 · 953 · 1076 · 1078 · 1083 · 1086 · 1097 · 1174 · 1204 · 1251 · 1260 · 1281 · 1287 · 1288 · 1289 · 1290 · 1291 · 1293 · 1294 · 1306 · 1332 · 1333 · 1335
Epistemology (60) — knowledge, belief and evidence — justification and rational credence, the value of knowledge, testimony, trust and expertise, and social and inductive-risk questions about evidence (group: philosophy): 023 · 053 · 142 · 143 · 146 · 148 · 151 · 225 · 242 · 267 · 273 · 290 · 295 · 317 · 321 · 326 · 327 · 347 · 353 · 401 · 404 · 415 · 422 · 433 · 438 · 442 · 451 · 491 · 506 · 537 · 550 · 556 · 569 · 572 · 577 · 596 · 601 · 610 · 615 · 633 · 637 · 639 · 647 · 649 · 810 · 814 · 829 · 834 · 845 · 855 · 857 · 864 · 877 · 884 · 943 · 1072 · 1084 · 1173 · 1174 · 1216
Logic (38) — valid inference and its formal theories — propositional and model-theoretic structures, proof and consequence, and inferentialist accounts of meaning (group: philosophy): 020 · 024 · 037 · 041 · 042 · 127 · 162 · 255 · 341 · 347 · 353 · 362 · 367 · 371 · 373 · 374 · 380 · 387 · 389 · 462 · 493 · 516 · 535 · 544 · 595 · 619 · 642 · 647 · 649 · 665 · 698 · 725 · 807 · 1064 · 1094 · 1142 · 1150 · 1239
Philosophy of mathematics (5) — what mathematics is about and how we know it — mathematical structuralism and ontology, the nature of proof and construction, and its history from Descartes to Kant and after (group: philosophy): 032 · 038 · 401 · 604 · 729
Philosophy of language (18) — meaning, content and reference as philosophy poses them — theories of meaning, meaning holism, assertion and whether machines assert, and conceptual change (group: philosophy): 044 · 050 · 089 · 159 · 162 · 444 · 490 · 511 · 518 · 547 · 606 · 625 · 638 · 665 · 667 · 1240 · 1278 · 1279
Religion (2) — religion as a subject — its relation to science, religious belief and practice, and how religious practitioners are treated: 866 · 1246
Anthology candidate (63) — a curation flag, not a subject — somebody judged the Anthology of the SOTA may want this work as well; it stays here unless a transfer is decided, and is never a primary topic (ADR-005, ADR-048; group: flags): 078 · 080 · 082 · 083 · 084 · 085 · 086 · 087 · 092 · 104 · 105 · 106 · 107 · 108 · 109 · 110 · 111 · 112 · 113 · 114 · 115 · 116 · 117 · 175 · 180 · 181 · 209 · 210 · 211 · 212 · 213 · 246 · 331 · 342 · 421 · 425 · 481 · 496 · 504 · 509 · 510 · 521 · 557 · 566 · 578 · 675 · 683 · 718 · 736 · 741 · 779 · 781 · 782 · 788 · 790 · 794 · 798 · 825 · 828 · 1172 · 1185 · 1187 · 1188
By status: The current account (737) · Offered (609) · Not yet judged (0) · Disbelieved (5) · Replaced (1)
What the status column means in this scheme — the words are luria’s, the meanings are this project’s.
| Status | Means | |
|---|---|---|
Active | The current account | The best explanation the record holds for why this happens |
Proposed | Offered | Stated and plausible, on evidence that is suggestive rather than settling — the document says what would settle it |
Deferred | Not yet judged | Filed because the question is real; no position taken on the answer |
Rejected | Disbelieved | Tested and failed, or contradicted by later work — and the thing it explained may still work perfectly well |
Superseded | Replaced | A later account covers the same ground better, and this one names it |
| # | Title | Summary | Status |
|---|---|---|---|
| THEORY-001 v4 | On a finite augmentation space, InfoNCE, logistic and spectral contrastive losses share one population optimum: the positive-pair density ratio | Johnson, El Hanchi & Maddison (2023), LIT-258 — over unconstrained functions on a finite augmentation space, the population minimizer of the spectral contrastive and NT-Logistic losses is K⁺ = p⁺(a₁,a₂)/(p(a₁)p(a₂)), and a minimizer of NT-Xent/InfoNCE over symmetric functions, with negatives i.i.d. from the marginal, is K⁺ up to a factor constant on communicating classes; that form is taken from van den Oord et al., not derived. It is a statement about the unconstrained optimum, not about what a network reaches. | Proposed |
| THEORY-002 v7 | Convergence of representations, in the Platonic hypothesis’s sense, is convergence of kernels, which fixes representations only up to the symmetry group of what is observed; whether closeness in distribution implies closeness of representation depends on the distance used | An inference joining Huh et al.’s Platonic hypothesis (ANTH-LIT-458) to Nielsen et al. (LIT-253) and Harvey, Larsen & Williams (LIT-250). It does not refute the hypothesis; it says what the hypothesis can and cannot mean. | Proposed |
| THEORY-003 v3 | Maximizing HSIC between representations and image identity maximizes the average squared MMD between the images’ view distributions, whose kernel mean embeddings exist by the Riesz representation theorem | Li, Pogodin, Sutherland & Gretton (2021), LIT-248, eq. 5 and App. B.2; Muandet et al. (2017), LIT-260, Lemma 3.1 — the one place in this family where Riesz is invoked explicitly. InfoNCE is not HSIC: Li et al.’s eq. 28 decomposes it exactly as −HSIC plus a log-mean-exp term, and Theorem B.1 bounds it with no variance assumption. | Active |
| THEORY-004 v8 | A representation is determined by its centred kernel up to a translation and an orthogonal transformation, and the rotation-aligned distance between two representations equals the Bures distance between their kernels | Harvey, Larsen & Williams (2023), LIT-250, Thm 1; Jorgensen & Tian, LIT-259, Remark 1.34 and Cor. 1.35, which name the kernel-to-Hilbert-space construction as GNS and state its minimal realizations unique up to a unitary (proof left as an exercise). This is the GNS connection the owner asked about, stated. | Active |
| THEORY-005 v4 | The positive-pair density ratio is the kernel of the conditional-expectation operator on L²(p), so spectral representations are that operator’s eigenfunctions, well defined when the positive-pair χ²-divergence is finite | An inference assembled on 2026-09-26 from Johnson, El Hanchi & Maddison (LIT-258), Tosh, Krishnamurthy & Hsu (LIT-251) and HaoChen et al. (LIT-249), with a two-line derivation of the record’s own. Johnson et al. write the operator formulation on a finite space (App. E.2); no source states it with its integrability condition. | Proposed |
| THEORY-006 v4 | InfoNCE is a lower bound on mutual information for every critic and can never exceed the log of the batch size | Poole et al. (2019), LIT-246, §2.3, Eqs. 8–10 — an exact proof (CPC’s own derivation, ANTH-LIT-589, passes through an approximation). Tschannen et al. (LIT-247) show that tightening the bound does not explain what makes the representations good. | Active |
| THEORY-007 v4 | Kernel PCA under the positive-pair density ratio recovers the eigenfunctions of the positive-pair Markov chain, and their top span is minimax-optimal for linear prediction of approximately view-invariant targets | Johnson, El Hanchi & Maddison (2023), LIT-258, Thm 3.2 and Thm 4.1 — proved for finite augmentation spaces at the population level, Thm 4.1 for d at least the number of communicating classes. HaoChen et al.’s spectral loss is the same factorization of the normalized positive-pair adjacency. Whether trained networks land on these eigenfunctions is not shown. | Active |
| THEORY-008 v5 | On a finite set of stimuli, what a regularized linear readout can decode from a representation is a function of its normalized kernel, and CKA, CCA and GULP are averages of readout agreement | Harvey, Lipshutz & Williams (2024), LIT-257, eqs. 2, 7–8, Prop. 2, Cor. 1 and Table 1 — proved identities. This is the finite-dimensional content of “a probe is a functional”: the probe’s output is fixed by the kernel, whatever orthonormal basis the representation is written in, for G = aC_X + bI; under any linear change of basis only for the CCA member, G = C_X. | Active |
| THEORY-009 v7 | In the positive-pair spectral self-supervised papers, self-adjointness comes from the symmetry of the positive-pair distribution, not from the Riesz representation theorem; elsewhere in the family it comes from a symmetrized loss, a precondition on the kernel, or composing the conditional-expectation operator with its adjoint | An inference from how the spectral SSL papers (LIT-258, LIT-249, LIT-252, LIT-242) obtain their eigenbases: each uses a symmetric pair matrix or kernel, and none invokes Riesz. In all but Simon et al., whose loss is symmetrized by hand, and Pfau et al., whose SpIN takes symmetry as a precondition on the kernel k, that symmetry is the symmetry of the positive-pair distribution. Answers the owner’s “do we even need Riesz?” for this family of results. | Active |
| THEORY-010 | Grangier and Auffèves’s contextual objectivity is an ontological postulate, not contextuality in either formal sense: its one argued consequence, unpredictability after a change of context, is reproduced by an epistemically restricted classical model | Places Grangier & Auffèves (2018), LIT-077, against the two formal notions (LIT-016, LIT-003) and against Spekkens’s epistricted models (LIT-007). The placement is the record’s, joining NOTE-044’s reading with LIT-007 and LIT-016; Grangier’s own derivations are not held. | Proposed |
| THEORY-011 v4 | Generalized contextuality is strictly broader than Kochen–Specker contextuality: a qubit already has no preparation-noncontextual model, though no Kochen–Specker argument with sharp measurements exists in dimension two | Spekkens (2005), LIT-266, §III and §IV, read in full in NOTE-748; restated in Budroni et al. (LIT-263, §IV.E, read in NOTE-844). Corrects the reading that contextuality needs dimension three. The dimension-two limit holds for sharp measurements only. | Active |
| THEORY-012 v8 | An empirical model is Kochen–Specker-noncontextual exactly when its context distributions glue to one global distribution, and since signed global sections always exist for no-signalling models, negative probability does not mark contextuality | Abramsky & Brandenburger (2011), LIT-016, Thm 8.1 with Prop 3.1, and Thms 5.4 and 5.9 — proved for finite measurement scenarios with no-signalling built into the definition. The graded version, the contextual fraction (LIT-265), is read (NOTE-236): CF = 0 exactly when this criterion holds. The review that places this formulation among its equivalents is read (NOTE-844); it asserts the equivalence with citations and does not show it. | Active |
| THEORY-013 v3 | Once context-dependent marginals are separated from contextuality, the behavioural, social and word-meaning data published as contextual show none | Dzhafarov, Zhang & Kujala (2015), LIT-264 — Contextuality-by-Default applied to five data sets, including primed word combinations from the quantum-cognition literature. Seeded, not yet read closely. The authors call general absence a working hypothesis, and later work in the same programme is reported to find behavioural contextuality. | Proposed |
| THEORY-014 v3 | In both formalisms of contextuality, classicality is the existence of a nonnegative version of a linear representation that always exists over the reals, so negativity is universal and only its unavoidability is nonclassical | An inference joining two proved results: LIT-016 Thms 5.4 and 5.9 with Thm 8.1, and LIT-003 Thm 2.8 with Cor 3.5. Each half is proved and read; the parallel is the record’s own, and LIT-003 attempts no comparison with LIT-016. | Active |
| THEORY-015 v3 | Kochen–Specker noncontextuality is measurement noncontextuality plus outcome determinism for sharp measurements, and preparation noncontextuality implies that determinism, so every Kochen–Specker proof refutes universal generalized noncontextuality while measurement noncontextuality alone is consistent with quantum theory | Spekkens (2005), LIT-266, §III, §VIII.A (Eqs. 77–88), §VIII.B, §IX — the bridge between the record’s two contextuality threads, which no held work states. Read in full in NOTE-748, which confirmed the §VIII.A proof and its need for the full preparation set. Joining it to the sheaf form (LIT-016) is the record’s inference. | Active |
| THEORY-016 v3 | An operational theory admits a generalized-noncontextual model exactly when its GPT admits a positive quasiprobability representation, and for a tomographically local theory any diagram-preserving such model is an exact frame with exactly as many ontic states as the GPT’s dimension | Schmid et al. (2020), LIT-003, Prop 3.2, Prop 3.4, Cor 3.5, Thm 4.1, Cor 4.2, Prop 4.3 — proved. Spekkens’s odd-d stabilizer Wigner representation (LIT-007) is a worked instance. The theorem gives no test for whether a positive representation exists. | Active |
| THEORY-017 v6 | In a Hilbert-space model only unitarily invariant structure is intrinsic; a basis or tensor factorisation, and so any parts or features, is extra data supplied from outside the space, and the record’s Hilbert-space works differ in where they get it | Carroll (2021), LIT-123: a quantum theory is fixed up to unitary equivalence by the Hamiltonian’s spectrum, and subsystems come from a factorisation that the dynamics must select. Van Rijsbergen (LIT-262) computes only traces and inner products, and treats each observable’s eigenbasis as a “point of view”. DisCoCat’s ε/η composition (LIT-273) is orthogonally covariant, while its Frobenius sequel (LIT-272) stipulates a basis and composes by elementwise product in it. THEORY-004 is the same point for learned representations. This is a synthesis across the four, not a result any one of them states. It does not say that basis-dependent models are wrong; it says what they have assumed. | Active |
| THEORY-018 v4 | Softmax training identifies a language model’s final-layer representation only up to an invertible linear map, so no inner product on it is intrinsic, and Park, Choe and Veitch’s causal inner product is fixed by a stipulation | Park, Choe & Veitch (2023), LIT-304, prove the invariance γ ↦ Aγ + β, λ ↦ A⁻ᵀλ (eq. 3.1). They choose M = Cov(γ)⁻¹ by setting a free diagonal D = I, and admit they have no principle for choosing D. NOTE-302 derives, and the filer re-checked, that Cov(γ) alone is compatible with every positive-definite M. So the paper’s remark that most inner products are ruled out holds only once the true concept directions are known. Under superposition (LIT-323) no inner product can make all features orthogonal. | Active |
| THEORY-019 v4 | Symmetry forces spectral degeneracy but degeneracy does not identify a symmetry: an operator commuting with a group has eigenspaces built from its real irreducibles, so abelian rotation groups force pairs over ℝ, and the spectrum fixes neither the group nor a basis inside a multiplet | Peter & Weyl (1927), LIT-329 §3, build representations as eigenspaces of an invariant kernel, and Kondor & Trivedi, LIT-305 Lemma 6, show that intertwiners preserve isotypic components. Neither states the degeneracy corollary or its converse. This document puts that together from several readings, and that assembly, with its proof, is now the record’s own claim, CLAIM-385; what stays here is the reading. It adds the real-scalar correction in NOTE-282, found in the reading of LIT-362, and the counting in the reading of LIT-346. It does not support “degeneracy detects symmetry”: a spectrum is consistent with several groups and says nothing about the characters inside a multiplet. | Active |
| THEORY-020 | Every Boolean algebra is the clopen algebra of its Stone space of prime ideals, and a finite one is the power set of its atoms, so a single Boolean context always has two-valued valuations and the Kochen–Specker obstruction lies in how contexts overlap | Stone (1936, 1937), LIT-353 and LIT-358: every Boolean ring is isomorphic to the compact open sets of its prime-ideal space, a totally disconnected, locally compact Hausdorff space that is compact exactly when there is a unit, and every such space arises this way. Kochen & Specker (LIT-298, Thm 0) turn this into the criterion that a partial Boolean algebra embeds in a Boolean one iff its two-valued homomorphisms separate points. The joining of the two, that non-classicality needs more than one context, is the record’s. Neither Stone paper uses “ultrafilter” or states a duality of categories. | Active |
| THEORY-021 v2 | In the exact configurations of uniform superposition (regular polygons, the tetrahedron, antipodal pairs, and tegum products of these that span the hidden space, with equal norms within each factor) the features form a rank-one POVM compressed from the n-feature basis: their dimensionality-weighted projectors sum to the identity | Elhage et al. (2022), LIT-323, found that features in uniform superposition settle into polytopes and tegum products, with feature dimensionalities clustering at 3/4, 2/3, 1/2, 2/5 and 3/8. The tight-frame and POVM reading is the reader’s inference in NOTE-278, checked numerically there. It was refined when filing: a tegum product is not globally tight, but the Dᵢ-weighted POVM still sums to the identity. None of this is in the paper. It does not make superposition contextual or quantum, and it says nothing yet about trained real models. | Active |
| THEORY-022 v4 | The reverse-engineered grokking network computes modular addition by multiplying characters of ℤ/p at a few frequencies, the same real two-dimensional irreducibles later found as circles in language models; in both the group comes from the task, not the network | Nanda et al. (2023), LIT-345, show that a one-layer transformer trained on addition mod 113 embeds its inputs at five key frequencies. It forms cos/sin(w_k(a+b)) and reads out Σ_k α_k cos(w_k(a+b−c)). The reading in terms of characters and irreducibles is NOTE-283’s, joined here to Engels et al.’s circles (LIT-322). It holds for one weight-decay model and its variants: dropout-trained generalisers are not Fourier-sparse. It is not evidence that a network discovered the group, which was given, or that the frequencies could be read off a spectrum. | Proposed |
| THEORY-023 v4 | Current evidence cannot settle whether an AI system is conscious: mimicry undercuts behavioural evidence and architectural indicators presuppose the disputed computational functionalism, so the dispute is over what counts as evidence as well as the answer | Birch (2025), LIT-111: behavioural markers are “gamed”, and architectural markers are “Janus-faced”, giving a two-level deadlock. Schwitzgebel (LIT-191) argues mimicry undercuts but does not rebut, and that the functionalist theories face minimal instantiation. Seth (LIT-135) makes conscious AI conditional on functionalism plus substrate flexibility. Butlin et al. (LIT-056) assume functionalism. The readings agree the question is currently unsettleable. They contest whether that is permanent and which way the prior leans. This says nothing about whether any AI is conscious. Block (2002, LIT-639) argues that for a perfect functional duplicate on another substrate we lack even a conception of the evidence; Block (2009, LIT-632) states the biological premise from the other side. | Proposed |
| THEORY-024 v2 | Classical Boolean logic is restored when a presheaf of contextual data acquires a global section or is sheafified | Ghose (2025), LIT-276 — asserts that the Heyting algebra of truth values “becomes Boolean” when the presheaf data collapse to a global section, and that sheaves encode Boolean reasoning. Both claims are asserted, not proved. The record’s readings refute them. The internal logic of a topos is fixed by the base category and its topology, not by whether one presheaf has a section (Isham–Butterfield, LIT-325, §6). Sheaf toposes such as Sh(ℝ) are not Boolean (NOTE-249). The contextuality criterion itself is untouched. | Rejected |
| THEORY-025 v2 | Neither utility information nor resource holdings, alone or together, can register claims that arise from how differently people convert resources into what they can do and be: equal resources leave unequal capabilities, and utility adapts to deprivation | Sen (1979), LIT-289, first-hand: a contented disabled person has no marginal-utility claim, no total-utility deficit and no primary-goods deficit, yet an evident claim. The 1998 lecture (LIT-282) names four sources of conversion variation. The negative thesis rests on one case and a shared intuition, and Sen says it stands without his positive proposal. The resourcist reply (Pogge) is not held, and the claim does not say capabilities are the right replacement. | Proposed |
| THEORY-026 v4 | For a system driven without feedback through fixed kernels, the average work dissipated at each switch of the drive equals the memory that fails to predict the next input; that is nonnegative when the drive is Markov and, summed, bounds the protocol’s dissipation from below when each kernel keeps its equilibrium stationary, so there only nonpredictive memory is wasteful; with feedback, in one binary channel no predictive agent is efficient | Still, Sivak, Bell & Crooks (2012), LIT-327: β⟨W_diss⟩ for the switch x_t → x_{t+1} equals I[s_t;x_t] − I[s_t;x_{t+1}] (Eq. 14, an identity). Under a Markov drive this nostalgia is nonnegative, and summed it lower- bounds dissipation when each kernel keeps its equilibrium stationary; both conditions are unstated in the paper and derived here. Fiderer et al. (LIT-041) show that with feedback, in one binary channel, predictive, max-entropy-action and efficient agents are disjoint. The claim is an ensemble average, not a per-operation floor. Whether the bound fails without the two conditions is QUESTION-191. | Active |
| THEORY-027 | Two individually decisive people, weak Pareto and an unrestricted domain cannot all hold, even when choice need only yield a best element; unlike Arrow’s theorem, the conflict is not removed by interpersonal comparability | Sen (1970), LIT-285: no social decision function satisfies U, weak Pareto and minimal liberalism. The proof was checked in this record, including the unproved one-way strengthening. Sen (1998), LIT-282: the paradox, unlike Arrow’s, is not resolved by interpersonal comparisons. The theorem is settled. Whether pairwise decisiveness is what liberty is remains open, and the record reads the rights-as-game-forms literature only through Sen’s reply to it. | Active |
| THEORY-028 v2 | The expected bias of any data-dependent choice, and the expected generalisation error of any learning algorithm, is at most √(2σ²·I) for σ-subgaussian losses, where I is the information the output carries about the data | Russo & Zou (2015), LIT-356, Prop. 1: |E[φ_T − µ_T]| ≤ σ√(2·I(T;φ)) for any selection T among σ-sub-Gaussian statistics. Xu & Raginsky (2017), LIT-347, Thm 1: |gen| ≤ √(2σ²·I(S;W)/n) for any algorithm P_{W|S}. Both proofs rest on Donsker–Varadhan and were checked by the readers. The bound is in expectation only. It is vacuous for deterministic learners on continuous hypotheses, where I(S;W) is infinite, and for any real network when I is bounded by counting bits. It is tight only for Gaussian argmax and threshold selection. | Active |
| THEORY-029 v5 | A higher-order attitude cannot make a motive the agent’s own by its order alone: any attitude specified without presupposing the agent’s participation can itself be disowned, and any specified to include it presupposes what it was meant to explain | Velleman (1992), LIT-295: every candidate for the agent’s standpoint in a hierarchical account (second-order desire, Watsonian value, decisive commitment) is either disownable or question-begging. Buss & Westlund (LIT-296) state the regress as their own argument; McKenna & Coates (LIT-291) and Dryden (LIT-297) credit it to Watson 1975, which the record has not read. Frankfurt’s own 2004 lectures (LIT-293) never address it. The dilemma is argued by examples, not proved, and it does not show that higher-order structure is irrelevant to agency. | Proposed |
| THEORY-030 v3 | For a memory evolving reversibly with its environment, Landauer’s bound prices only steps that lose logical distinguishability, at least k ln 2 of entropy per bit lost, exported to the environment and not necessarily as heat, so copying onto a blank register, measuring or evaluating a bit has no minimum cost; learning a label has a floor only in total entropy production, at least the information learnt, which in Goldt and Seifert’s perceptron can be paid in the weights’ own entropy with vanishing heat | Bennett (2003), LIT-360: the cost attaches to many-to-one maps of the logical state, at least k ln 2 of entropy per bit exported to non-information-bearing degrees of freedom, which “need not” be heat. The record derives it for a memory and environment evolving reversibly from an uncorrelated start: the environment’s entropy rises by at least the logical entropy lost, H(X | f(X)), and an injective step has no floor, attained exactly by a permutation. Goldt & Seifert (LIT-308) bound information learnt by total entropy production, payable with vanishing heat in their toy model. It does not license a k_BT ln 2 heat floor per judgment, per gradient step or per bit learnt. Whether the bound survives without reversible dynamics is QUESTION-215. | Active |
| THEORY-031 | The likelihood-ratio detector is optimal under the payoff, Neyman–Pearson and posterior criteria, which differ only in its threshold, so performance is an ROC and the criterion a point on it; d′ is criterion-free only for equal-variance normal signal and noise | Peterson & Birdsall (1953), LIT-364 — the threshold on ℓ = f_SN/f_N is optimal for expected value and at fixed false-alarm rate, and the two optimum families coincide (Part I Thms 1–7). The ROC’s slope equals the threshold (Thm 8). Tanner & Swets (1954), LIT-368, carry this over to the human observer as d′ plus a criterion. Stanislaw & Todorov (1999), LIT-367, state that d′ varies with the criterion unless the variances are equal. The separation of sensitivity from bias is a property of the model, not of the data. | Active |
| THEORY-032 | The Yoneda lemma determines an object only up to isomorphism, from its whole hom-functor, among objects the category already has; as a formal version of “an object is determined by its relations” it presupposes the relata | nLab, Yoneda lemma (rev. 2026-08-17), LIT-221 — y is fully faithful and y(c) ≅ y(d) iff c ≅ d, and pointwise bijections of hom-sets without naturality do not suffice. Lam & Wüthrich (LIT-222) state two of its consequences without the name. The philosophical reading, a relational criterion of identity up to isomorphism rather than a construction of objects from relations, is the record’s own. It does not say that the lemma supports eliminating objects. | Active |
| THEORY-033 v2 | The measured noise scale B_simple tracks the critical batch size within about 10× on six of eight tasks and about 20× on two generative models, so the gradient’s noise-to-signal ratio sets the critical batch only as far as the local quadratic model with an optimal step holds | McCandlish, Kaplan, Amodei et al. (2018), LIT-348: under a local quadratic model with an optimal step, per-step progress is ΔL_max/(1 + B_noise/B). This gives the steps–examples hyperbola and B_crit = E_min/S_min. The Hessian-free B_simple = tr(Σ)/|G|² is the batch at which gradient noise equals signal, and it tracks B_crit within about 10× on most of eight tasks, missing by about 20× on two generative models. The authors call the derivation one with “unfounded assumptions”. Nothing in it is information-theoretic, and its temperature ε/B is not k_BT. | Proposed |
| THEORY-034 v3 | Chakravartty’s dilemma reaches only structural realisms that keep relata but deny them every intrinsic identity-fixing feature, and of the seven structural-realist texts read here against it, two are of that kind: Floridi’s informational structural realism and Esfeld and Lam’s moderate structural realism | Chakravartty (2012), LIT-196 — non-eliminative OSR must choose eliminativism or a role for intrinsic features in identity, and the no-priority variant fares no better. The placements of the record’s other OSR texts on that map are the record’s own synthesis, from NOTE-192, NOTE-095, NOTE-099, NOTE-189 and NOTE-142. The account does not say the dilemma is sound, and it does not say eliminative OSR survives; the chapter itself leaves eliminative OSR untouched. Whether the founding texts are of the target kind is QUESTION-336. | Active |
| THEORY-035 v5 | Deep networks generalise because the diffusion phase of SGD compresses each layer’s information about the input | Shwartz-Ziv & Tishby (2017), LIT-324, report a fitting phase followed by a long compression phase in the information plane, and read compression by gradient diffusion as the mechanism of generalisation. Their §3.4 reports that with 5% of the data compression lowers I(T;Y). Saxe et al. (2018), LIT-372, rerun their code and find the compression phase only in double-saturating networks measured through an imposed binning, find it under full-batch GD as under SGD, and find compression and generalisation in all four combinations. The account is rejected. The IB functional of LIT-338, the tanh two-phase observation and the gradient-SNR transition are not. | Rejected — Saxe et al. show the compression phase appears only for double-saturating units under an imposed binning or noise model, occurs under full-batch GD as under SGD, and dissociates from generalisation in all four combinations; the paper’s own small-sample run already showed compression losing label information |
| THEORY-036 v2 | Dennett’s real-pattern criterion, compressibility against the bit map, admits almost every non-random pattern; the projectibility, perspective and scale-relativity that rainforest realism needs are later additions that do the ontological work | Dennett (1991), LIT-220 — a pattern is real “if there is a description of the data that is more efficient than the bit map, whether or not anyone can concoct it”. Ladyman (LIT-219) replaces this with indispensability to projectible generalisations, perspective- and scale-relative and lossy. Separating the two, and the claim that the added clauses carry the exclusions, is the record’s reading. The definition that would confirm it (ETMG) is unread. | Proposed |
| THEORY-037 v3 | In the topos programme quantum propositions form a distributive Heyting algebra, not an orthocomplemented lattice, and its negation is a pseudo-complement under which excluded middle can fail | Döring & Isham (2007, II), LIT-335 — daseinisation maps each projector injectively to a clopen sub-object of the spectral presheaf, with δ(P∨Q) = δ(P)∨δ(Q) but only δ(P∧Q) ⪯ δ(P)∧δ(Q). The orthocomplement is carried to inner daseinisation, not to ¬δ(P). That Sub_cl(Σ) is Heyting (Thm 2.5) is sketched in the source, and the record re-derives it: each Σ_V is extremally disconnected, so Sub_cl(Σ) is a frame. Paper I (LIT-343) chooses intuitionistic deduction. Isham–Butterfield (LIT-325) state that the Heyting algebra is fixed by the base category. | Active |
| THEORY-038 | Category theory gives radical ontic structural realism no formal support: generalized elements exist in every category, morphisms relate objects the category presupposes, and Bain’s physical cases eliminate spacetime points, not relata | Lam & Wüthrich (2015), LIT-222, against Bain (2013), LIT-223. Bain’s “structure as object in a category” relabels relata rather than removing them, and his GR and TQFT cases dispose of points only. That the Yoneda lemma (LIT-221) strengthens the rebuttal is the record’s inference: no paper in the debate names it. This does not refute radical OSR. It removes one argument for it, and Eva 2016’s reply is unread. | Proposed |
| THEORY-039 v2 | The later phases reported in neural-network training differ in kind: after the transition a network may simplify its weights, acquire item-specific information, lose generalisation, confine its tangent kernel or saturate its units, and none of these is a measured compression of I(X;T) | Nanda et al. (2023), LIT-345, Zucchet et al. (2025), LIT-371, Saxe et al. (2018), LIT-372, Prakash & Martin (2025), LIT-369, and Zhou et al. (2025), LIT-370, each report training as a sequence of phases. Their phases are defined by different quantities and fall at time scales from 10² to 10⁷ steps. What follows the transition differs in kind from work to work. Two of them, the two with a mechanistic intervention, show a circuit forming while the loss is flat. Only one measures I(X;T), and there the later fall belongs to the estimator. This is the record’s synthesis across the five, not a claim any of them makes. | Proposed |
| THEORY-040 v5 | A condition on free agency stated only in present psychological structure is met by a manipulated agent, so the account must count that agent free or add a historical condition, and no historical condition in the record’s readings is shown to escape | McKenna & Coates, LIT-291: every “mesh” compatibilism can be installed by a manipulator, and Frankfurt is quoted (2002, second-hand) accepting that a manipulated character leaves a person responsible. Dryden (LIT-297) and Buss & Westlund (LIT-296) make the same point against hierarchical autonomy. Historical supplements are reported to face “loading-in” and a circularity worry; neither is argued in full in the record. The claim says what the account must choose between, not which choice is wrong. | Proposed |
| THEORY-041 | Birkhoff and von Neumann proposed the modular law, not orthomodularity, and proved it fails for closed subspaces in infinite dimension; Husimi used the orthomodular identity only as an unnamed proof step | Birkhoff & von Neumann (1936), LIT-306 — the lattice of closed subspaces is orthocomplemented and not distributive. They propose modularity (L5), motivated by a dimension function, and give an explicit infinite-dimensional pentagon that breaks it. The word “orthomodular” does not occur. Husimi (1937), LIT-357, derives modularity as the parallelogram law under a finite-chain assumption and uses the orthomodular identity as a step without naming it. Citing either paper for “the orthomodular lattice of quantum logic” misattributes it. | Active |
| THEORY-042 | Under a superselection rule a coherent superposition across sectors is operationally a mixture, because no observable connects the sectors; Wick, Wightman and Wigner proved such a rule for integer versus half-integer spin and only postulated it for charge | Wick, Wightman & Wigner (1952), LIT-339 — they define a superselection rule and show that a superposition across sectors “is not a pure state, but a statistical mixture”. They prove the rule from time reversal for integer versus half-integer angular momentum, and postulate it for charge with “no conclusive evidence”. What follows for Birkhoff–von Neumann’s lattice (LIT-306), a product of sector lattices with central sector projections, is the record’s inference. The centre-of-the-algebra formulation belongs to Haag, who is not read. | Active |
| THEORY-043 v6 | A mind of mindless agents and a mind of minded agents are one functionalist move run in two directions, and what separates them is an anti-nesting principle or an architectural criterion, neither yet principled | Minsky’s society of mind builds a mind downward, out of agents that are not minds. Schwitzgebel (LIT-159) builds a candidate mind upward, out of agents that are. The readings agree that agency survives both directions: Block grants a homunculi-head beliefs, List grants organised groups agency and awareness, Levin finds nested goal-pursuing collectives (his “Selves”) at every scale. The dispute narrows to phenomenal consciousness, and every published way to accept the downward move while refusing the upward one is either an anti-nesting principle (Putnam’s stipulation, IIT’s exclusion postulate, Kammerer’s functional version), each introduced for or justified weakly by the verdict it gives, or an architectural criterion that would count against a loosely coupled society of mind as much as against a nation. Proposed: an account of where a dispute stands, from philosophical argument and no measurement. | Proposed |
| THEORY-044 v2 | In relational frame theory the self is verbal behaviour’s content, its process and its context, and the self as context is a perspective learned from deictic relations that cannot itself be found as content | Barnes-Holmes et al. (LIT-541) define three selves: the conceptualized self, the content of verbal relations about oneself; the knowing self, their ongoing process; and the transcendent self, their context. Hayes et al. (LIT-555) say the third arises from deictic frames (I–you, here–there, now–then) as “a sense of self as a locus or perspective”, and is “a context for verbal knowing, not the content”, so its limits “cannot be consciously known”. The account maps the three onto the record’s holdings: the content is the narrative self (Dennett, Gallagher, Strawson), and the context is what Hume could not find among his perceptions and what Metzinger calls a transparent perspective. It differs from the minimal self (Gallagher) on origin: RFT says the perspective is learned in language. The evidence for the learned origin is cited, not read, so Proposed. The clinical claim is THEORY-051. | Proposed |
| THEORY-045 v3 | Felt affect is the experience of the body’s regulatory state, valenced by what that state means for staying alive and present throughout waking experience, not only in emotion; whether what is felt is a prediction of that state or a map of it is unsettled | Barrett (2017), LIT-542, and Damasio & Carvalho (2013), LIT-388, are two independent accounts that agree on a base layer. What is felt as affect (valence and arousal for Barrett, feeling for Damasio) is the body’s regulatory state. Its valence is that state’s value for the organism, and it is present in hunger, pain and well-being as much as in emotion. They disagree about what the experience is of. For Barrett it is the brain’s allostatic prediction of the body, issued from agranular limbic cortex. For Damasio it is a topographic map of the body’s state, built in the upper brainstem, and their paper makes no use of prediction. Seth (LIT-135) builds on the same base but makes his claim about consciousness, not about affect. Friston (LIT-526) supports neither. Proposed: both sources are theoretical syntheses, and neither tests the claim. | Proposed |
| THEORY-046 v2 | Expected tangible rewards for merely engaging in an interesting task lower later free-choice engagement with it | Deci, Koestner and Ryan (1999, LIT-557): across 55 experiments, expected tangible rewards given for working on an interesting task lowered free-choice engagement after the reward stopped (d = −0.40; children −0.43, college students −0.21), and lowered self-reported interest less (−0.15). By their study-by-study account, Cameron and Pierce’s rival analysis found the same for this contingency (performance-independent rewards, −0.29), while disputing nearly everything else. Their 2001 reply (LIT-562), read here, re-codes 145 studies and finds it again: rewards offered for doing an interesting task lowered free choice, −0.35 across 57 studies. Active: both sides of the dispute find this effect. | Active |
| THEORY-047 v2 | A regulation taken in under controlling conditions is introjected rather than integrated, so the social history of how a value was acquired shapes how autonomous acting on it is | Deci and Ryan (LIT-558) and Ryan and Deci (LIT-559): supports for relatedness and competence are enough to get a value internalized, but only as an introject or a compartmentalized identification; integration also needs autonomy support. The experimental evidence is Deci et al. (1994), as reported: the same amount of internalized behaviour correlated positively with felt freedom and enjoyment under autonomy support and negatively under control. Field studies on parenting, religion and medical training agree, correlationally. This is a historical condition on autonomy of the kind THEORY-040 asks about, with empirical support, but it has not been tested against matched present endorsement or applied to manipulation. | Proposed |
| THEORY-048 | In explaining psychiatric disorder, biological findings implement psychological functions rather than replacing them | Kendler (2008), LIT-539: following Marr, a lower-level theory either replaces a higher-level construct (temperature by mean kinetic energy) or implements it, and in psychiatry biology “will implement but not replace psychology”. The thesis is argued from neuroscience’s successes in perception, learning and memory, not from a psychiatric case, so it is Proposed. It is a thesis about explanation, not about distinct mental causes: it survives Pernu’s argument (LIT-147) that the neural evidence supports only mental causation by identity. Kendler 2005 (LIT-552), which argued the mind–brain propositions this paper develops, is unread. | Proposed |
| THEORY-049 v2 | Whether an external event lowers or raises intrinsic motivation depends on whether it is experienced as controlling or as information about competence | Cognitive evaluation theory, as tested by Deci, Koestner and Ryan (1999, LIT-557) and summarized by Ryan and Deci (LIT-559) and Deci and Ryan (LIT-558): rewards, feedback, deadlines and choice affect intrinsic motivation through their “functional significance”. Controlling events shift the perceived locus of causality outward and undermine it; informational ones affirm competence and enhance it, but only with a sense of autonomy. The meta-analytic pattern fits, and controlling versus informational positive feedback differ by d = −0.78 in four studies. Mediation by felt control is untested for rewards. Its rival, Cameron, Banko and Pierce’s account (LIT-562), finds rewards tied to a score or to beating others do not undermine. Neither side has tested mediation. | Proposed |
| THEORY-050 | Psychological inflexibility, in which verbal relations give private events aversive functions and make experiential avoidance a general strategy, is a transdiagnostic process in psychopathology | Hayes et al. (LIT-555) model psychopathology as inflexibility: cognitive fusion supports experiential avoidance, which narrows behaviour. Barnes-Holmes et al. (LIT-541) give the mechanism: once a word stands in derived relation to an event it can carry that event’s aversive functions, so private events become worth avoiding. Kashdan and Rottenberg (LIT-553) find inflexibility across depression and anxiety in cognitive, behavioural and physiological systems, and say its causal role is unknown. The evidence is correlational, small, mostly self-report and mostly from the model’s authors, and the meta-analysis that would test it (LIT-543) is unread, so Proposed. It is compatible with the loop account of disorder, not a rival to it. | Proposed |
| THEORY-051 v4 | Strengthening the self as context, a perspective from which thoughts about oneself are held as thoughts, is a process by which acceptance and commitment therapy reduces suffering | ACT names the self as context as one of its six processes: from it “one can be aware of ones own flow of experiences without attachment to them”, so it fosters defusion and acceptance, and mindfulness exercises and metaphors foster it (Hayes et al., LIT-555). RFT reads defusion as moving thoughts from I HERE NOW to I THERE THEN, a deictic shift (Barnes-Holmes et al., LIT-541), labelled “no more than a heuristic”. No study in the record tests the self as context as a process. Its only support is borrowed from small defusion studies under RFT’s reading, so Proposed on weak grounds. The conceptual account of the self is THEORY-044. | Proposed |
| THEORY-052 | Frustration of the needs for autonomy, competence and relatedness is a transdiagnostic process in psychopathology | Vansteenkiste, Ryan and Soenens (2020, LIT-561) propose that need frustration, distinct from mere lack of satisfaction, plays “a transdiagnostic role”, citing a longitudinal study in which it predicted adolescents’ depressive and eating symptoms and “largely accounted for their co-occurrence”. Deci and Ryan (LIT-558) had located the etiology of “various forms of psychopathology” in developmental need deprivation, with need substitutes, controlled styles and rigid patterns as the route. The evidence is correlational, mostly self-report, and from the theory’s authors. A partner of the inflexibility account, not a rival. | Proposed |
| THEORY-053 | A treatment’s efficacy is not evidence for its theory of change: only change in the theorised process that is specific and comes before the outcome bears on it, and moving the process without moving the outcome counts against the theory | Salkovskis, Sighvatsson and Sigurdsson (LIT-538): “The effectiveness of a treatment is not evidence for the validity of the theory on which it is based”, with one exception, that changing the theory’s crucial factor without changing the problem disconfirms it. Hofmann and Hayes (LIT-544), from the other wing of CBT: a model whose process cannot be shown to apply “is incorrect and needs to be set aside” even if the intervention works, and a procedure that fails to move the process leaves the model untested. Active because it is close to a logical point and both state it. What it does not say is that mediation proves a mechanism; both sources deny that. | Active |
| THEORY-054 v3 | A regulation is autonomous to the degree it is integrated with one’s other values and needs: autonomy is graded, and is not set by the order of the attitude that endorses it | Self-determination theory orders motives on a continuum from external through introjected and identified to integrated regulation and intrinsic motivation. Ryan and Deci (LIT-559) and Deci and Ryan (LIT-558) place autonomy in integration, “congruence with one’s other values and needs”, and report a quasi-simplex structure and an experiment in which integrated and introjected internalization behave differently. Ryan and Deci (LIT-560) align this with hierarchical accounts but grade it. It is the empirical counterpart of THEORY-029’s negative claim. It is not shown that integration can be measured apart from endorsement, and it does not escape Velleman’s dilemma. | Proposed |
| THEORY-055 | An appraisal of an event’s pertinence to the agent’s concerns elicits the emotion, as a state of action readiness, and emotions differ by their mode of action readiness | Frijda, Ridderinkhof & Rietveld (2014), LIT-540, Frijda’s own late statement of the theory of The Emotions (LIT-546, unread). An automatic appraisal of how an event bears on one’s concerns elicits a state of action readiness: a motive to change one’s relation to the object, with control precedence. Emotions differ by mode (hostility for anger, avoidance for fear), and “in the absence of concern pertinence … no emotion”. It is the record’s only read statement of an appraisal theory, because Lazarus (LIT-550) is unread. Both the elicitation claim and the claim that emotions differ by mode are argued, and neither is tested. The second is partly definitional within the theory. Rivals THEORY-057: both accounts let instances vary and group them by function, but the appraisal account puts the unity in the agent’s readiness and the constructionist account puts it in the perceiver’s concept. Proposed. | Proposed |
| THEORY-056 v3 | Emotion regulation is not a process separate from emotion generation: most of it is one motive state checking another, with no distinct regulating system above them | Frijda, Ridderinkhof & Rietveld (2014), LIT-540, deny “the exclusivity of emotion regulation processes”. Appraising the consequences of an impulse raises a competing readiness, as when fear of retaliation holds back anger, so control is the interaction of motive states and not reason governing emotion. Barrett (2017), LIT-542, reaches the second half from the opposite side of the emotion debate: automaticity and control are “different brain modes … not two battling brain systems”, and she offers as a hypothesis that reappraisal works by the same predictions that construct emotion. Two rival theories of what an emotion is agree on this. Gross (1998), LIT-554, poses the question and keeps the distinction. Proposed: argued from examples and from architecture, untested. | Proposed |
| THEORY-057 | Emotion categories are populations of variable instances grouped by the perceiver’s concepts, not natural kinds with a shared neural or appraisal mechanism | Barrett (2017), LIT-542: degeneracy, population thinking, and a table of findings in which no region, network, pattern or neuron is consistent for an emotion category. From these she concludes that categories such as fear are populations of variable instances, grouped by a goal and constructed by categorization with a concept. She rejects basic-emotion and causal appraisal theories as positing a “Lockean essence”. This is the record’s only read statement of the view. The record’s philosophy holdings sharpen it. Pernu (LIT-147) shows that many-to-one realisation at a fine grain does not rule out one variable at a coarser grain, so degeneracy alone does not carry the conclusion, and Table 1 has to. Searle (LIT-482) shows that Barrett’s comparison with money is to observer-relative function, not to institutions. Rivals the appraisal account, THEORY-055. Proposed: one theoretical paper, no independent test, and the reply unread. | Proposed |
| THEORY-058 v2 | Mental disorders are maintained by self-reinforcing causal loops rather than expressing a latent common cause, which is how they can outlast their triggers | Three traditions that do not cite one another for it put self-sustaining loops where a latent cause would be. Borsboom (LIT-547) makes disorder an alternative stable state of a strongly connected symptom network, kept up by hysteresis after its trigger has gone. Salkovskis, Sighvatsson and Sigurdsson (LIT-538) make it a threat meaning protected by the behaviour it drives. Kendler (LIT-539) finds causal loops across levels, from genes to culture. The convergence is real; the evidence is indirect, simulated or clinical, and none of it is an individual time series showing hysteresis, so the account is Proposed. It says nothing about what starts a disorder. | Proposed |
| THEORY-059 | The readiness potential does not show that a neural decision to act precedes awareness of the urge to act | Libet read the readiness potential, which begins half a second or more before a spontaneous movement and before the reported urge, as the brain deciding first. Two independent arguments in the record remove that inference. Schurger, Sitt & Dehaene (LIT-605) show that a leaky accumulator driven by noise and fitted to waiting times alone reproduces the averaged readiness potential (r² = 0.96), because movement-locked averaging recovers the fluctuations that crossed threshold; a prediction of theirs held in 13 people. Dennett & Kinsbourne (LIT-431) argue that the clock report times a represented content, not an event in the brain. Proposed: the authors say their model shows the potential could be fluctuation, not that it is. It says nothing about whether the urge causes the act. | Proposed |
| THEORY-060 v2 | A life story constructed from adolescence on is the form a person’s diachronic identity takes, and its content shapes later well-being | McAdams (2019), LIT-595: narrative identity is “a person’s internalized and evolving story of how he or she has become the person he or she is becoming”, which gives a life “unity, moral purpose, and temporal coherence”. It arrives in adolescence and young adulthood, on the back of autobiographical memory and autobiographical reasoning, as the third layer of a psychological self after the actor of traits and the agent of goals. Stories with agentic and redemptive themes go with well-being and generativity, and in one longitudinal therapy study the story “changes first, and then the storyteller gets better”. A review essay: every finding is cited, not shown, and it concedes that having a life story may be a modern cultural construction. Strawson’s “Against Narrativity” (LIT-452) denies the first half for many people. | Proposed |
| THEORY-061 | In evidence-accumulation tasks, goals and instructions act on a decision by setting the parameters of the accumulation (drift, starting point or baseline, and threshold), not by specifying the response, and this holds for when to act as well as for which | Bogacz et al. (LIT-569) define cognitive control, in a two-choice task, as the adjustment of drift, starting point and threshold to maximise a utility. Ratcliff and McKoon (LIT-576) find that the manipulations behave that way: speed or accuracy instructions are fitted by boundary separation alone, stimulus proportions mainly by starting point, difficulty by drift alone. Schurger et al. (LIT-605) carry the picture to the decision of when to move: the task goal raises the baseline toward threshold and leaves the moment to fluctuation. The convergence is real; the evidence is group fits on a few paradigms, so Proposed. It does not say who sets the parameters, or how. | Proposed |
| THEORY-062 | Model-based and model-free predictions both operate in instrumental and in Pavlovian learning, and which one controls behaviour follows their relative reliability, not the preference of a supervising system | Daw, Niv & Dayan (LIT-580) cast habitual and goal-directed instrumental control as model-free caching and model-based search, and let behaviour follow whichever estimate is less uncertain; simulations reproduce the effects of over-training, task complexity and reward proximity on devaluation. Dayan & Berridge (LIT-584) show from instant revaluation of a salt cue that Pavlovian prediction also has a model-based form, and suggest the same reliability arbitration there. Both controllers pursue the same ends; neither is the irrational one. The instrumental half is qualitative simulation; the Pavlovian half of the arbitration is a suggestion. Proposed. | Proposed |
| THEORY-063 | The unity of experience is the integration of one global world-model into a single functional cluster, and it does not require a self-model | Metzinger’s précis of Being No One (2005), LIT-568: the globality constraint makes every conscious content part of one world-model. On the functional level that is “highest-order binding” into a single causal role, and on the neural level the prediction of “one single area of maximal causal density”, after Tononi and Edelman’s dynamic core. “What you subjectively experience upon experiencing your world as coherent is the high internal correlation strength between a subset of physical events in your own brain.” A unified world comes before a self: the minimal case is “Selfless Snapshot Consciousness”, and fully depersonalized states are “non-subjective consciousness”. The neural half is a cited hypothesis, the précis says little is known, and how the cluster becomes one subject’s is left open. | Proposed |
| THEORY-064 | What is experienced as a self is the content of a self-model the system cannot recognise as a model, and nothing beyond such models is a self | Metzinger’s précis of Being No One (2005), LIT-568, with his encyclopedia article “Self models” (LIT-450): a phenomenal self is a transparent self-model, one whose representational character “is not accessible to subjective experience”, so that the system experiences its content “simply as ourselves”. Selfhood is “a function realized by a lack of information”, and “no such things as selves exist in the world”. Transparency is graded, and the perspective itself is modelled, as a phenomenal model of the intentionality relation. Two things are offered: a prediction (a wholly opaque self-model would abolish selfhood) and an ontological stipulation. The précis adds no evidence; its case studies are in the book, unread. | Proposed |
| THEORY-065 | The unity that makes a movement an agent’s action is achieved by conformity to the constitutive norms of agency, not given by the causal unity of a mind, so collective agents are agents in the same sense as individual ones | Korsgaard (2014), LIT-587: an action is a movement “backed by the agent as a whole”, and ordinary attribution implies that the agent was active and that the action expresses who she is. Following the categorical and hypothetical imperatives gives action the form of self-determined efficacy; the content of the maxims chosen under that form constitutes practical identity. Self-consciousness of one’s own attitudes breaks the unity an animal is given, and reason is the work of rebuilding it, so unity of agency “is an achievement, not a given”, and people can act together “in the most literal sense”. The Tanner Lectures (LIT-564) supply the reflective structure the chapter assumes. Argued, with the Kantian premise assumed and the collective mechanism stated in a paragraph. | Proposed |
| THEORY-066 | A Markov-blanket partition is defined relative to a chosen internal set, so a graph has one around almost any set of nodes, and the formalism alone does not say which set is the system | The formal core of Bruineberg et al.’s critique (LIT-603, C4 in NOTE-447). In a directed acyclic graph the blanket of a node set A is its parents, children and the children’s other parents, and A is conditionally independent of everything outside A and its blanket. That holds for every A, so any set whose blanket leaves something outside gets a valid internal, blanket and external partition. Having a blanket therefore picks out no set. In Friston’s soup (LIT-526) the set was picked by spectral clustering with k = 8, not by the blanket. Active because it is a short derivation that anyone can check. It covers graphical (Pearl) blankets and the 2013 procedure. It does not cover the later sparse-coupling definitions at nonequilibrium steady state, which the record has not read. | Active |
| THEORY-067 | Self-control over time needs no faculty of will: interests that dominate at different delays bargain, and resolve is the recursive staking of expected future choices on the present one | Ainslie’s précis (LIT-586): hyperbolic discounting makes a smaller, sooner reward temporarily preferred, so successive “interests” conflict as in a repeated prisoner’s dilemma. Treating a choice as a precedent bundles the series, and summed hyperbolic curves favour the larger, later rewards; a lapse costs credibility. Will is that recursion, not an organ. Schelling (LIT-602) describes the same divided chooser from the side of tactics: we manage our later selves as we manage other people. The mathematics of bundling is sound; that willpower works this way is argued, and the précis concedes it is hard to test directly. It is a claim about how control is achieved, not about whose control is self-governance. | Proposed |
| THEORY-068 v2 | In a two-alternative choice made by two competing leaky accumulators, the decision is optimal only when leak and mutual inhibition balance, so that the network integrates the difference of the evidence without loss; imbalance bounds accuracy at any fixed time and weights early or late evidence | Bogacz et al. (LIT-569) prove that the pure drift diffusion model is the continuum limit of the sequential probability ratio test, and so the optimal two-choice decider, and that the linearised Usher–McClelland network reduces to it exactly when leak equals inhibition (and, for free response, when both are also large). Usher and McClelland (LIT-565) derived the difference of the two units as an Ornstein–Uhlenbeck process with net leak K = k − β: K ≠ 0 caps accuracy, leak-dominant weights late evidence and inhibition-dominant early. Active because the core is derivation, checkable on paper. What it does not say: that brains are balanced, that the result carries to more than two options or to non-stationary evidence, or that the primacy and recency seen in six participants are explained by it. | Active |
| THEORY-069 v4 | Rhythmic bimanual coordination switches from anti-phase to in-phase through a nonequilibrium phase transition in relative phase, captured by the HKB equation, with critical fluctuations and critical slowing as early warning | Kelso’s 2021 retrospective (LIT-601) states the Haken–Kelso–Bunz model: relative phase φ between the hands obeys dφ/dt = −a sin φ − 2b sin 2φ, so in-phase and anti-phase are both stable for b/a > 1/4 and anti-phase loses stability below it as movement speeds up. With noise the switch is a nonequilibrium phase transition, and the reported data show enhanced fluctuations and critical slowing before it. Many effectors act as one through a collective variable, with no controller choosing the pattern. Proposed, because the relaxation-time and hysteresis data are not read first-hand. | Proposed |
| THEORY-070 | How much cognitive control to exert, and on what, is decided by a cost-benefit computation (the expected value of control) in a specification system distinct from the structures that implement the control | Shenhav, Botvinick & Cohen (LIT-585) unify dACC’s many reported functions as one: deciding whether, where and how much control to allocate. A control signal has an identity (a task set, a threshold, an attention template) and an intensity; its expected value is its probability-weighted payoff, with future value discounted, minus an intrinsic cost rising with intensity. dACC monitors and specifies; lateral prefrontal and subcortical structures implement. The paper reviews evidence and fits nothing, so Proposed. It does not say what the cost is, how EVC is computed, or that it governs emotion regulation. | Proposed |
| THEORY-071 v3 | Minimal agency requires individuality, interactional asymmetry and self-generated normativity, and individuality without the other two is not agency | Barandiaran, Di Paolo & Rohde (2009), LIT-566, read in NOTE-458. The three conditions are that the system distinguishes itself from its environment with no observer doing it, that it is the active source of modulations of its coupling with the environment, and that it regulates that coupling against norms its own organisation sets. Each is necessary, and together they are claimed to be sufficient. Individuality is the precondition of the other two and does not suffice. A cell in passive osmosis, a kitten warmed by its mother and a person with a Parkinsonian tremor are each individuals, and none of them is acting. The generative definition is an open autonomous organisation that adaptively modulates its coupling so as to maintain itself. Here “autonomy” and “self” mean organisational closure. They do not mean a subject or self-governance. Proposed: a conceptual analysis checked against intuitive cases, with an asymmetry criterion its authors call incomplete. | Proposed |
| THEORY-072 v4 | Organisms differ from dissipative structures such as a candle flame not by far-from-equilibrium self-maintenance, nor by circular self-maintenance alone, but by organisational differentiation: several distinct constraints that produce one another at different time scales | The record’s first answer to the demarcation question that NOTE-094 reports. Prigogine (LIT-516) supplies the dissipative structures, and nothing in his account separates them from organisms. Mossio, Saborido & Moreno (2009, LIT-570) grant a candle flame organisational closure. Its one macroscopic pattern keeps up the conditions of the combustion that makes it. They draw the line at organisational differentiation: in an organism several distinct structures make distinct contributions, where a flame makes “a unique contribution”. Montévil & Mossio (2015, LIT-582) narrow closure to mutual dependence among constraints. Each constraint must be both produced by and productive of another, with at least one slow and one fast dependence. On the record’s reading, that builds differentiation into closure, as Mossio and Bich (2014) already say of closure of constraints. No paper analyses a flame under the 2015 definitions. Neither paper says closure defines an organism. | Proposed |
| THEORY-073 v2 | In Friston’s 2013 formulation and the applications the record holds, a Markov blanket does not individuate a system: where it falls is fixed by modelling choices made before it is traced (the coupling graph, the internal set and the time at which steady state is assumed), and a blanket read from a fixed graph is the same whether the system produced the boundary or it was imposed | Bruineberg et al. (LIT-603) and Raja et al. (LIT-598) argue, by different routes, that the Markov blanket of the free-energy literature is placed and not found. The formal core is THEORY-066: the partition takes the internal set as input. This account adds what the critiques show about practice. In Friston’s soup (LIT-526) the graph was built from one kind of coupling and steady state was assumed when the run stopped. In published applications the blanket sits wherever the model needs it: in the receptors of a brain, the membrane of a bacillus, the beam joining two pendulums. The formalism also gives the same description to a membrane the cell makes and a beam nobody’s states make. So the blanket presupposes the boundary it is offered as the criterion of. Active since 2026-10-27, narrowed to the 2013 formulation and the applications held. The later steady-state definitions have not been read, and the unrestricted claim is THEORY-1097, Proposed. | Active |
| THEORY-074 | Implicit accessibility of the true self-concept is not what self-report scales of authenticity or of need satisfaction measure, though those two self-reports are not shown to be separate constructs | Schlegel, Hicks, Arndt & King (2009), LIT-606: true-self accessibility, the speed of “me” judgments for traits a person takes to be her true self, correlated .05 with AI-3 authenticity and .20 with basic need satisfaction (N = 124), and each predicted meaning in life independently. The authors read this as showing the constructs differ, and concede the difference is confounded with method, reaction time against self-report. The two self-reports correlated .52, and felt autonomy was only one third of the need-satisfaction composite, whose autonomy items include “I can pretty much be myself”. So the paper separates the implicit measure from both self-reports, and does not separate authenticity from autonomy. Proposed: one sample for the correlations, method unresolved. | Proposed |
| THEORY-075 | Obligation is the reflective rejection of what would violate the agent’s practical identity, and moral obligation follows only because valuing any practical identity commits the agent to valuing her humanity | Korsgaard (1992), LIT-564: because human consciousness is reflective, an agent must act on reasons, and so must identify with some law, a “practical identity”: “a description under which you value yourself”. “Your reasons express your identity, your nature; your obligations spring from what that identity forbids.” Obligation is “the reflective rejection of a threat to your identity”, unconditional where violation would be worse than death. Identities are a “jumble” and differ across social worlds, so this much yields no morality. Moral obligation enters because valuing any identity requires valuing one’s humanity, the source of all one’s reasons. “The Normative Constitution of Agency” (LIT-587) later makes practical identity the content of maxims chosen under the formal norms. Argued, with the key steps flagged by their author as sketchy; the commentaries and reply are unread. | Proposed |
| THEORY-076 | Diachronic self-governance is constituted by cross-temporal links of intention that are intrapersonal analogues of shared intention, not by narrative unity and not by intertemporal bargaining | Bratman (2018), LIT-567: an agent governs herself over time when she is self-governing at each time along a planned activity and her intentions at those times interlock as the intentions of people acting together do, so that she acts “together” with herself. Her standpoints include a conditional, reflexive end of her own diachronic self-governance, which is what lets resolve against temptation be self-governed while following through on Kavka’s toxin is not. He rejects the bargaining model (McClennen, Ainslie) in two sentences and calls narrative unity less basic in one. A philosophical model argued from cases; the analogy is partial by its author’s account and its terms come from a book the record has not read. | Proposed |
| THEORY-077 v2 | Goals pursued for identified or intrinsic reasons receive more sustained effort, which carries their better attainment, and attaining them raises well-being more than attaining goals pursued under pressure | Sheldon & Elliot (1999), LIT-589: a goal is self-concordant to the degree its reasons are identified or intrinsic rather than external or introjected. In two semester-long student samples, self-concordance predicted sustained effort, and effort fully carried its link to attainment (self-concordance β = .02 and .08, ns, with effort in the model). In the same two samples attainment raised well-being more when goals were self-concordant (interaction β = .11, .23), partly through accumulated daily experiences of autonomy, competence and relatedness. Everything is self-report and correlational, and the structural models fit only after revision. It is evidence for the autonomous end of SDT’s continuum, not for integration as distinct from identification. | Proposed |
| THEORY-078 v2 | The top C eigenvalues of a trained C-class classifier’s Fisher are carried by the second moment of its class-mean logit derivatives, so a cut at the bulk edge keeps the span of the class means, and they stand clear of the bulk to the extent between-class separation exceeds within-class variation | Papyan (2019), LIT-619: for softmax cross-entropy the Gauss–Newton matrix G, which is the model’s Fisher averaged over inputs, is an uncentred second moment of logit derivatives indexed by class and logit. It decomposes exactly into four terms (Eq. 28), and its top C eigenvalues match those of the class-mean term G₁. Papyan (2020), LIT-613, splits those C into one global-mean outlier and C − 1 between-class ones, finds a C(C − 1) cross-class mini-bulk beneath them, and proves the whole pattern for a Gaussian toy model. Papyan (2018), LIT-617, supplies the measurements and the attribution of the Hessian’s outliers to G. The decomposition is algebra. That G₁ carries the outliers is measured, by eye, under a training protocol narrower than practice. So this is Proposed. | Proposed |
| THEORY-079 v3 | Bayesian model reduction under the Laplace approximation prices the reductions of a singular parent model with a Gaussian Occam factor, so its free-energy differences can be wrong by a term that grows with log n | The filer’s synthesis, stated by no source. BMR’s closed form (Friston & Penny, LIT-620, Eq. 9; Friston, Parr & Zeidman, LIT-614, Eq. 11) charges a reduction through log-determinants of Gaussian precisions, which is MacKay’s regular Occam factor. Watanabe, LIT-616, says that models with hierarchical layers or hidden variables are singular, that no normal distribution approximates their posterior, and that their free energy grows as λ log n. BMR is applied to exactly such models: mixtures, hierarchical empirical Bayes and latent states. Neither literature cites the other. The exact identity is untouched (THEORY-081). The claim is about its Laplace form, and a test on reduced-rank regression would settle it. | Proposed |
| THEORY-080 v3 | In a linearised network with a Gaussian prior on its parameters, the Occam factor is a sum over the NTK’s eigenvalues, so on spherical data each harmonic pays ½ log(1 + βnµ_k/α) and the kernel’s eigenvalue decay schedules the complexity penalty across frequencies | The filer’s synthesis, stated by no source. Its exact half is filed as the record’s own claim, CLAIM-384; what stays here is the spherical account. A network linearised at initialisation, with an isotropic Gaussian prior on its parameters and Gaussian noise, is MacKay’s linear-in-parameters model (LIT-623). Its Occam factor is −½ Σ log(1 + βλ_a/α) over the eigenvalues of JᵀJ. These are the empirical NTK’s, which on uniform spherical data form Bietti & Bach’s degree blocks, nµ_k with multiplicity N(d, k) (LIT-608). Degrees whose βnµ_k exceeds α pay about ½ log n per harmonic, and degrees below pay almost nothing. With µ_k ~ k^(−d), the number of paid directions γ grows as n^((d−1)/d), not as the parameter count. Basri et al.’s bound (LIT-612, Eq. 14) is the matching data-fit term. The kernel’s decay exponent is the schedule of the penalty. | Proposed |
| THEORY-081 v2 | The evidence of any model formed from a full model by changing only its prior is the full evidence times the full posterior expectation of the prior ratio, so the Savage–Dickey ratio is its point-mass case and choosing which parameters to keep is evidence maximisation over the prior | Friston & Penny (2011), LIT-620, Eq. 3: if models share a likelihood and differ only in priors nested inside a full prior, then p(y|m_i) = p(y|m_F)·E_{p(θ|y,m_F)}[p_i(θ)/p_F(θ)]. Their Eq. 6 is the point-mass case, the Savage–Dickey ratio that Wagenmakers et al. (2010), LIT-609, derive from the other end, and that Dickey (1971), LIT-610, stated in this form for any continuous likelihood. Friston, Parr & Zeidman, LIT-614, restate it for any new prior and give conjugate closed forms. Active because the identity is three lines of Bayes’ rule that anyone can check. The two Savage–Dickey conditions turn out to be the same condition. The identity is exact. Its Laplace and variational forms are only as good as the full posterior, and with no constraint on the prior family the optimum is maximum likelihood. | Active |
| THEORY-082 | Steepest descent is defined only relative to a metric, and Amari’s proof that natural-gradient learning is Fisher efficient needs the Fisher information at the optimum to be invertible, the condition whose failure WBIC calls singular; in a multilayer perceptron it fails wherever an output weight is zero | Amari (1998), LIT-607. Theorem 1 is a Lagrangian derivation: under |dw|² = Σg_ij dw_i dw_j the steepest-descent direction is −G⁻¹∇L, so it changes with G. Theorem 2 shows that online learning with step 1/t along the Fisher natural gradient attains the Cramér–Rao bound G⁻¹/t, and its proof uses G(w*)⁻¹. Watanabe, LIT-616, Eq. 14, calls a truth regular when the optimum is one point and its Fisher is positive definite, and singular otherwise. From Amari’s own Eq. 6.12, the score for hidden unit i’s input weights carries the factor v_i. So the Fisher of a multilayer perceptron loses rank wherever an output weight is zero. That set is part of the optimum whenever the teacher needs fewer hidden units than the student has. Active because each step is checkable in the two texts. The claim that the Fisher is the only invariant metric is Chentsov’s, cited and not held. | Active |
| THEORY-083 v3 | In Papyan, Han and Donoho’s runs of VGG, ResNet and DenseNet trained with cross-entropy on seven balanced datasets without augmentation, training past zero error shrinks last-layer within-class variability against between-class variability, and moves the centred class means and the classifier toward a common simplex equiangular tight frame and the decision toward nearest class mean, nearly to completion on the four easier datasets and only partly on ImageNet | Papyan, Han & Donoho (2020), LIT-618, measured 480 trained classifiers on seven datasets with VGG, ResNet and DenseNet. Through the terminal phase, within-class variability of last-layer features falls (NC1), and the centred class means become equinorm and equiangular with cosine −1/(C − 1) (NC2). The classifier aligns with them (NC3), and the decision becomes nearest class mean (NC4). They prove that NC1 and NC2 imply NC3 and NC4 for the MSE-optimal and max-margin classifiers, and that the simplex ETF is the unique error-exponent-optimal codebook. Read from the plots, collapse is close to complete on the four easier datasets and partial on ImageNet at the last epoch. Papyan (2020), LIT-613, sees class means separate and grow more orthogonal with depth. The measurements cover one protocol, and the dynamics are unexplained outside free-features models. Within them, THEORY-278 (LIT-974) derives collapse for MSE under a re-whitened flow, and THEORY-286 (LIT-994) gives the cross-entropy endpoint under class imbalance. The paper’s further claim, that the Hessian’s class outliers are a symptom of collapse, is argued and not measured, and is left to THEORY-078. | Active |
| THEORY-084 v3 | Because the Gauss–Newton Fisher JᵀJ and the NTK Gram matrix JJᵀ share their non-zero spectrum, the lazy-regime Fisher of a ReLU network on spherical data inherits the NTK’s harmonic-degree blocks, and a spectral threshold on it is well posed only at gaps between blocks | The filer’s synthesis, stated by no source. The identity is linear algebra: JᵀJ (parameters × parameters) and JJᵀ (samples × samples) have the same non-zero eigenvalues. Under squared loss JᵀJ is the Gauss–Newton matrix and the Fisher. JJᵀ is the empirical NTK Gram matrix, which in the kernel regime on uniform spherical data has the degree-block spectrum of Bietti & Bach (2021), LIT-608: µ_k with multiplicity N(d, k). The threshold claim draws on Cao et al. (2019), LIT-624. Their guarantees are stated only for whole eigenspaces, with sample costs that grow as the gap below them shrinks. It also draws on Basri et al. (2019), LIT-612, where a structural zero block shows up in a finite sample as small non-zero eigenvalues. No paper filed computes a Fisher spectrum in this regime. | Proposed |
| THEORY-085 v2 | A classifier’s class-driven Fisher outliers pair each class’s feature mean with that class’s own error mean, so K-FAC’s single Kronecker product of class-averaged factors adds every cross-class pairing and misplaces them | Papyan (2020), LIT-613: per layer, the Fisher is a weighted sum of Kronecker products of features and backpropagated errors (Eq. 7.5), and its class outliers come from class means of gradients that are approximately h_c ⊗ δ_c. K-FAC (Martens & Grosse 2015, LIT-622) multiplies the class-averaged feature covariance by the class-averaged error covariance. Papyan finds its outliers and mini-bulks “drastically misaligned”, and the class-wise CFAC aligns much better at deep layers. The identity relating the two, CFAC − K-FAC = the class-weighted between-class covariance of the factors, is the record’s own and is filed as CLAIM-391. The evidence for the mechanism is one MLP, spectra only, judged by eye. | Proposed |
| THEORY-086 v2 | In the kernel regime gradient descent fits the target eigenspace by eigenspace of the neural tangent kernel, at rates set by their eigenvalues; on uniform spherical data the eigenspaces are the harmonic degrees, and for fully connected ReLU networks the non-zero eigenvalues decay as k^(−d) at every depth | Three derived results that compose. Cao et al. (2019), LIT-624, Theorem 4.2: for a wide two-layer ReLU network, the training residual’s component in the top-r_k NTK eigenspace falls as (1 − λ_{r_k})^T, for any target. Basri et al. (2019), LIT-612: on uniform spherical data the Gram matrix is a convolution, so its eigenvectors are harmonics, with closed-form eigenvalues per frequency. The bias-free kernel is zero on odd frequencies k ≥ 3, and a bias restores them. Bietti & Bach (2021), LIT-608, Corollary 3: the L-layer ReLU NTK decays as k^(−d) on S^(d−1), the same exponent at every depth. Active for the kernel regime on uniform spherical data, where every step is proved. It says nothing about networks whose kernel moves. | Active |
| THEORY-087 v3 | The Bayesian complexity penalty grows as (d/2) log n in a regular model, where the curvature at the optimum sets the Occam factor, and as λ log n in a singular one, where λ is the real log canonical threshold; with the prior positive on the optimal set, λ falls below d/2 when that set is infinite or has a point of degenerate curvature, and equals d/2 when it is finitely many points of non-degenerate curvature | MacKay (1992), LIT-623, writes the evidence as best-fit likelihood times an Occam factor, the ratio of posterior to prior accessible volume, which under a Gaussian approximation is P(w_MP)(2π)^{k/2} det^{-1/2}A. When the likelihood dominates, det A grows as n^d, so the penalty is (d/2) log n. Watanabe’s WBIC paper, LIT-616, recovers that case (Lemma 3, Theorem 5) and states what replaces it when the Fisher information is degenerate at the optimum: λ log n − (m − 1) log log n, with λ the RLCT (Theorem 2). The regular half is re-derived by Laplace’s method with its conditions. The singular half is Watanabe’s cited theorem, checked by exact free energies in two singular models of known λ. The volume reading of λ is in Watanabe’s book, which is unread. | Active |
| THEORY-088 v2 | Slow large-scale activity in human cortex is organised as in a pattern-forming medium: its flow is set by interacting spiral defects centred on phase singularities, which sit on boundaries between functional regions, annihilate with spirals of opposite rotation and repel those of the same | Xu, Long, Feng & Gong (2023), LIT-638: in Human Connectome Project fMRI band-passed to 0.01–0.1 Hz, the cortical phase field holds about 16–19 spirals at a time around phase singularities, concentrated on boundaries between functional regions; their centres drift superdiffusively, opposite spirals annihilate (51% fully, 46% partly) and like ones repel (2.6%), and their positions and senses decode task condition above a raw-amplitude decoder. One source, fMRI only, at a spatial scale chosen because it maximised that decoding; the routing of activity flow is read from phase gradients and a phase-oscillator model, never perturbed. The kinship with Belousov–Zhabotinsky spirals and pattern-formation defects is the record’s analogy, not the paper’s. | Proposed |
| THEORY-089 | The content of a mental representation has two factors, a narrow conceptual role inside the head and a referential factor relating it to the world, and a long-arm role theory that gets Twin Earth truth conditions right reduces to the same two | Block (1986), LIT-648, and Block (1987), LIT-625. Meaning has a conceptual-role component “entirely ‘in the head’”, an expression’s “total causal role, abstractly described” in inference and decision, which twins share and which explains their behaviour, and an external component relating representations to referents and truth conditions. Conceptual role fixes the nature of the referential factor, not reference. A one-factor theory with long-arm roles must, to get Twin Earth truth conditions right, import normal context, causal chains of borrowed reference and experts; chop off what lies outside the skin and the rest is the short-arm role, so the difference is “merely verbal”. Social meaning is assigned to the referential factor or to a third, social factor, and is only sketched. Proposed: no identity conditions for roles, and narrow content is given room, not shown explanatory. | Proposed |
| THEORY-090 v2 | A basic, affective form of consciousness is realised subcortically, in the upper brainstem and thalamus, before and without cortex, and its first function is alarm: survival behaviour, care for the body and generalised one-shot learning, with no choice between options | Newen & Montemayor’s ALARM theory (2025), LIT-626: basic arousal, a sensitivity to pain, pleasure and other basic affect without focused attention, can be realised without cortex, by the upper brainstem and thalamus, and its function is to alarm the bodily agent when a homeostatic variable leaves its range, giving the signal “100% weight” through “rather rigid behavioural programmes without choices”. Damasio & Carvalho (2013), LIT-388, supply the subcortical clause independently: feeling is generated in the upper brainstem and the insula is not needed. Both papers argue from cited evidence and offer no new data, and neither has a marker that tells a felt alarm from an unfelt one. The function clause rests on ALARM alone, and Veit’s account rivals it. | Proposed |
| THEORY-091 | A deficit in which consciousness and a capacity are lost together does not show that the capacity is a function of phenomenal consciousness, since access is lost too and the capacity is one the machinery of access has | Block (1995), LIT-643, §6. Marcel, Flanagan, van Gulick and Schacter argue from the thirsty blindsight patient who does not reach for the water, and Searle from Penfield’s petit mal automatisms, that a function of phenomenal consciousness is to let information guide action. In blindsight access is missing too, and in petit mal nothing shows experience is missing at all. “The fallacy is: an obvious function of the machinery of access-consciousness is illicitly transferred to phenomenal consciousness.” That experience causes access, so that the function is experience’s after all, is “a bold hypothesis, not a fallacy”, and the deficit cannot decide it. Proposed: single-source, and the distinction it rests on is argued from conceivable cases. | Proposed |
| THEORY-092 v3 | Behavioural capacity does not fix intelligence: a system with the capacity to respond sensibly to every possible input can lack it, so whether behaviour is intelligent, or the mark of any mental property, depends partly on how it is produced | Block (1981), LIT-642: the strongest behaviourist conception of intelligence, a capacity to give sensible responses to any sequence of inputs, “whatever they may be”, is met by a machine that stores every sensible conversation of a test’s length and looks up its next reply, yet “the machine has the intelligence of a toaster”. So psychologism is true: two systems alike in all actual and counterfactual behaviour can differ in intelligence through the processing that mediates it. Block (1995), LIT-630, n. 1: the same machine refutes the wider claim that there is no mental difference without a behavioural one. It is a claim about constitution, not evidence: performance stays evidence for competence. It names no required kind of processing, and its machine is a lookup table, not a trained network. | Proposed |
| THEORY-093 v2 | A content of mind is conscious when a continuous flow of homeostatic feelings identifies it as the organism’s own; the feelings are conscious in themselves and hybrid, partly made of the body state they map, because interoceptive pathways let the body act directly on the neurons that map it | Damasio & Damasio (2022), LIT-628, an essay with no data, read only through a summarising fetch tool, so its wording is paraphrased here. Consciousness is the spontaneous identification of mind contents as belonging to one’s own organism, and a continuous stream of homeostatic feelings, from hunger and pain to a faint feeling of existing, supplies it; the feelings are conscious in themselves and confer consciousness on exteroceptive images. They are hybrid because interoceptive axons are unmyelinated, partly non-synaptic and outside a systematic blood–brain barrier, so viscera and circulating molecules act on the neurons that map them. Damasio & Carvalho (2013), LIT-388, read in full, supply the upper-brainstem site of feeling and the unmyelinated-fibre proposal. Proposed: the identification is a definition, the mechanism an interpretation of anatomy, and the clinical evidence does not separate this account from its rivals. | Proposed |
| THEORY-094 | Neither report nor no-report paradigms isolate the neural basis of consciousness, because post-perceptual cognition that tracks the percept persists without report; only a design that removes differential post-perceptual cognition does | Block (2007), LIT-646, framed the methodological puzzle: the neural basis of experience can be found only by deciding whether it includes the machinery of access, and the evidence comes through report. The no-report paradigm was the answer. Block (2019), LIT-637, argues it has “a fatal flaw”: subjects not asked to report still think about what they see, and that thought is aligned with the percept (the “bored monkey” problem). Eliminating report isolates the basis of experience “only if it eliminates post-perceptual cognitive processing” correlated with the percept. Brascamp et al.’s inconspicuous rivalry, whose switches subjects detected at chance, is the one such design Block offers. The method is specific to rivalry so far, and Block says there may be no general solution. | Proposed |
| THEORY-095 v3 | Phenomenal character is not fixed by long-arm functional role or by externally individuated representational content: on Inverted Earth it stays the same while both invert, so only internal accounts, short-arm functional or physical, remain open | Block (1990), LIT-634: on Inverted Earth colours and colour words are inverted, so a subject fitted with inverting lenses notices nothing. After long residence, or for a twin with a molecule-for-molecule identical brain raised there, the intentional content of the experience of the sky inverts and so does its long-arm functional role, while qualitative content stays the same; Q = F₁, Q = F₂ and F₁ ≠ F₂ breaks transitivity of identity. Block (2003), LIT-635, turns the case on externalist representationism: for colour there is no shared appearance property left to explain the sameness, and long-term memory blocks the gradual-shift reply, so “mental paint” is what stays the same. Proposed: both rest on an externalist shift of content and on first-person sameness, and Block concedes that a short-arm functional theory of qualia would escape. | Proposed |
| THEORY-096 | Perceptual consciousness is global availability: a content becomes conscious when the activity it drives into a core of long-range hub neurons, prefrontal among them, crosses a threshold and ignites it, so that the network amplifies, sustains and broadcasts that one content to the specialised processors; below threshold it leaves a decaying wave and is not experienced | Mashour, Roelfsema, Changeux & Dehaene (2020), LIT-631, a review by the theory’s proponents. Conscious access is “a non-linear network ignition” that amplifies and sustains a representation so that local processors can access it, in a distributed core of long-range layer II/III and V pyramidal neurons with prefrontal cortex a key hub but “not … the exclusive territory”. Ignition is exclusive: one content at a time. Evidence: seen and unseen trials diverge after about 200 ms across modalities; in van Vugt et al.’s monkeys, missed stimuli drove V1 and V4 but only reported ones, and false alarms, ignited sustained prefrontal firing, and the signal-detection threshold is the ignition threshold. The review adopts the premise that global availability “is what we subjectively experience as a conscious state”, and calls experience without access untested; that premise, not the access data, is where it rivals overflow and the sensory account. Single source, second-hand evidence, and the P3 question conceded open. | Proposed |
| THEORY-097 | Long-range coordination in the human forebrain is carried by brief ripples that co-occur at distant sites: during them neurons co-fire more whatever the distance between them, and at retrieval they carry stimulus-specific reinstatement of encoding co-firing | Verzhbinsky, Daume, Cheng, Rutishauser & Halgren (2026), LIT-633: in 1,373 single units from five bilateral forebrain regions of 35 epilepsy patients doing a Sternberg task, ripples (70–100 Hz, about 70 ms) co-occur between bundles at a median 5% at every tract distance from 71 to 223 mm, and unit pairs co-fire a median 34% more during co-ripples than in no-ripple periods, beyond a rate-only null and with no loss over distance. The gain rises with load (13% in maintenance, 19% at retrieval), and encoding co-firing for a stimulus recurs at retrieval in 0.29% of cell-pair trials in co-ripples against 0.14% outside them. Correlational throughout: one task, two load levels, clinically placed electrodes, nothing perturbed. | Proposed |
| THEORY-098 v4 | The neural basis of perceptual consciousness does not include the prefrontal machinery of cognitive access: it is recurrent activity in sensory cortex | Block’s “back of the head” position, from three papers. Block (2005), LIT-629: a phenomenal NCC (for seen motion, recurrent MT/V5–V1 activity) and an access NCC (frontoparietal broadcasting), with winner-take-all access letting a recurrent sensory representation lose and stay unaccessed. Block (2007), LIT-646: the mesh argument. If workspace activation is not part of the basis of experience, strong losing sensory coalitions explain why experience overflows access; if it is, nothing does. Block (2019), LIT-637: no-report designs do not settle the prefrontal question, because thought about the percept persists, and one design that removes it found no prefrontal difference by fMRI, which Block calls evidence against prefrontalism while granting that ECoG could still support it. Proposed: an inference to the best explanation, with every experiment second-hand and the decisive test not yet run. | Proposed |
| THEORY-099 | Tryptophan networks in microtubule architectures support collective superradiant excitonic states, and their thermal quantum yield rises with network size and survives static disorder of room-temperature size | Babcock et al. (2024), LIT-645: a radiative Hamiltonian of up to more than 10⁵ tryptophan transition dipoles, on tubulin geometry, predicts superradiant states up to about 4000 times the single-tryptophan rate in a centriole, and a thermal quantum yield that rises with network size and is almost unaffected by static disorder of about 200 cm⁻¹, though that disorder cuts the brightest state’s enhancement from about 3600 to about 20. Steady-state spectroscopy finds a tryptophan quantum yield of 17.6 ± 2.1% in microtubules against 10.6 ± 0.6% in tubulin dimers. No lifetimes were measured. This is not evidence for Orch OR or for any claim about consciousness. | Proposed |
| THEORY-100 | A neural correlate of conscious report does not require laminar cortex: in crows it is carried by the nidopallium caudolaterale, a nuclear pallial region whose neurons follow the reported percept rather than the stimulus | Maldarelli & Güntürkün (2025), LIT-650, reviewing Nieder et al. (2020): in crows reporting near-threshold stimuli, single neurons in the nidopallium caudolaterale (NCL), the functional analogue of prefrontal cortex, fired with the “seen” report whether or not a stimulus was shown and were silent on “not seen” reports. NCL is nuclear, not layered; the cortex-like layers and columns found in birds are confined to the sensory pallium. So a correlate of conscious report does not need laminar cortex. The crow evidence is second-hand, from one laboratory and not in the record, and a report paradigm cannot separate access from phenomenal consciousness. | Proposed |
| THEORY-101 v2 | Consciousness began as hedonic valence, which evolved as a common currency for trading off competing options in action selection among animals with many degrees of freedom | Veit’s pathological complexity thesis, as he restates and defends it in his reply to commentators (2025), LIT-105: consciousness originated as hedonic valence, “a common currency of sharing evaluative information across multiple control systems”, which animals with many degrees of freedom need to solve the combinatorial trade-offs of action selection. Felt valence is identical with that currency, “not Cartesian but cybernetic”. Motivational trade-offs are his criterion for consciousness. The source is a reply piece; the thesis is argued in a book the record has not read, and the mechanism is a sketch. ALARM (THEORY-090) rivals it on what the first consciousness did. | Proposed |
| THEORY-102 v3 | In Vishne, Gerber, Knight and Deouell’s intracranial recordings from ten epilepsy patients viewing clearly visible images for up to 1.5 s, the pattern of high-frequency activity across ventral temporal cortex carried image category, and exemplar identity among 60 images, in a time-invariant code for as long as the image stayed on while amplitude fell about 80%; at the sampled prefrontal and parietal sites, category content was a burst about 150 to 600 ms after onset that did not track duration | Vishne, Gerber, Knight & Deouell (2023), LIT-644: in 430 visually responsive subdural electrodes from 10 patients viewing images for 300–1,500 ms with no report on analysed trials, high-frequency activity and single-electrode category selectivity fell about 80% from peak by 800–900 ms, while the pattern across ventral temporal electrodes kept near-ceiling, time-invariant category and exemplar information that ended a fixed delay after the image went off. Prefrontal and parietal information was confined to about 150–600 ms and ignored duration. This met the predictions both IIT’s and the global workspace’s proponents registered for the paradigm, so it did not discriminate them. Above- threshold images only, sparse right-lateralised frontal coverage, one frequency band; it does not show the code tracks experience rather than input. | Active |
| THEORY-103 v3 | Perceptual consciousness overflows cognitive access: in partial-report tasks more items are experienced than the roughly four that working memory holds, though any one of them can be accessed when cued | Block (2007), LIT-646, and Block (2011), LIT-640. Subjects shown 8–32 items say they see all or almost all of them, report about 4, and when cued after offset can report or compare most of any cued subset: capacity 6–7 of 8 up to 1.5 s (Landman et al.), and 7, 6 and 5 of 8 at 1, 2.5 and 4 s (fragile visual short-term memory), against a working memory that stays at about 4. Block reads the surplus as experienced. The rival “sparse” reading holds it in an unconscious store plus a conscious generic or fragmentary image, and Block argues there is no independent evidence for either posit. Proposed: every experiment is second-hand, and that the surplus is conscious is the contested step. Overflow means most items are unaccessed, not that any is inaccessible. | Proposed |
| THEORY-104 v2 | Under distribution shift the best layer for a linear readout lies below the top: across the last layers of a trained network, in-distribution accuracy rises while out-of-distribution accuracy falls | Uselis & Oh (2025), LIT-678: linear probes on frozen intermediate layers of image classifiers beat last-layer retraining under shift, with zero-shot worst-group accuracy 79.4 → 87.1 (Waterbirds) and 56.0 → 82.0 (CelebA), layer 7 of 8 beating layer 8 on every subpopulation dataset, while in-distribution accuracy is best at the last layer. Chang, Deng & Chen (2025), LIT-657: in GPT-2 Small on a synthetic task, early-exit out-of-distribution accuracy peaks at layer 10 (56.90%) and falls to 50.00% at layer 12 while in-distribution accuracy climbs to 93.17%. The layer is chosen on out-of-distribution data throughout; ViT gains are small; the language-model evidence is one synthetic task; and Chang et al.’s information estimate is questioned in its NOTE. | Proposed |
| THEORY-105 v2 | For RoBERTa-base fine-tuned on English classification data, with loss measured by a linear probe refitted on the frozen encoder, points sampled from the convex hull of models fine-tuned on one dataset, one task family or twelve GLUE and SuperGLUE datasets lost no more than any model fine-tuned elsewhere and beat the group’s own members in 88% to 96.7% of comparisons, and the centroid of the general-level models was a better starting point for BitFit than the pretrained model | Gueta et al. (2023), LIT-658: RoBERTa-base models fine-tuned on the same dataset, the same task family, or any of 12 GLUE and SuperGLUE datasets cluster in weight space. Sampled points in the convex hull of each group beat the group’s own members in 88% to 96.7% of comparisons. Extrapolating past the members raises the loss quickly, so the members sit near the region’s edge and averaging moves inward. The paper calls the region convex, but shows only that the hull lies inside it, by a probe-based loss. Its reading of model soups and SWA as picking points inside the region is argued in its §8, not tested. Moving from the centroid towards the origin stays low-loss far past the members, which the authors cannot explain. Promoted 2026-10-20 on the probe-loss comparisons measured (ADR-047 v3); the geometric thesis is THEORY-828. | Active |
| THEORY-106 | In random-features ridge regression the double-descent peak is a divergence of the test error at the interpolation threshold 2N = n as the ridge goes to zero, which a positive ridge keeps finite and a ridge of the tuned size removes; minimum-norm linear regression has the same peak at n = d in exact finite-sample form | Liao, Couillet & Mahoney (2020), LIT-679: for random Fourier features with n, p and N large together, the test MSE has a closed form through a deterministic equivalent of the resolvent. As λ → 0 its corrections jump from O(1) to order 1/λ across 2N = n, det(Ω⁻¹) scales as λ, and the test error diverges at 2N = n unless the test data lie within about λ of the training data. At λ = 10⁻⁷ and 10⁻³ the curve has a singular peak; at the tuned λ ≈ 0.2 and at 10 it has none. Dereziński, Liang & Mahoney (2019), LIT-683: exact MSE of the minimum-norm estimator under a surrogate design, peaking at n = d with value σ² tr(Σ⁻¹), and below the threshold equal in expectation to ridge regression at the λn that makes the ridge effective dimension n. Proportional-limit theorems for one shallow model each; nothing here reaches trained deep networks. | Proposed |
| THEORY-107 | Merging models fine-tuned from one pretrained start loses accuracy through interference in parameter coordinates: redundant small updates dilute the influential ones, and influential updates of different models conflict in sign | Yadav et al. (2023), LIT-675: keeping only the top 20% of each task vector by magnitude loses almost nothing, so most of an update is redundant. Among the entries that remain, signs conflict between models, more so as more models are merged. Merging (IA)³ models with the multitask model’s signs reaches 72.0 against 73.1 for multitask training and 66.4 for TIES with elected signs. That is the strongest evidence that sign is the bottleneck. But the oracle signs come from training on every task’s data, the ablation finds rescaling and the disjoint mean matter more than election, and conflicts are as frequent among checkpoints of one task as across tasks. | Proposed |
| THEORY-108 | Across load and temperature, the connectivity and output similarity of independently trained solutions predict test accuracy where endpoint curvature does not: a flat but poorly connected landscape generalizes worse than a connected one of the same curvature | Yang, Hodgkinson, Theisen, Zou, Gonzalez, Ramchandran & Mahoney (2021), LIT-663: thousands of trained networks on a load by temperature grid, measured by the endpoint Hessian, by mode connectivity on a trained Bezier curve between two independent runs, and by CKA of their outputs. Phases III (flat, poorly connected) and IV-A (flat, connected) have almost the same Hessian and different accuracy; with 10% noisy labels the sharp, unconverged phases beat phase III; label noise barely moves the Hessian while connectivity and CKA fall. The best accuracy is in the flat, connected, high-similarity phase IV-B. The counterexamples are to the anthology’s ANTH-SOTA-012. One architecture family carries most of it, phases are read by eye, and connectivity alone also fails when the load is data amount. | Proposed |
| THEORY-109 v2 | The solutions SGD finds in a deep network lie in one connected low-loss set, joined by simple curves and spanning volumes of measurable dimension, and this is a property of the solutions training finds, not of every minimum | Garipov et al. (2018), LIT-673, and Draxler et al. (2018), LIT-653, found independently that minima of deep networks trained from different initializations are joined by paths of near-constant loss, a one-bend curve or an AutoNEB path, while the straight line between them climbs to near-chance error. Benton et al. (2021), LIT-656, widened curves to simplicial complexes joining up to seven modes and a low-loss region of at least 10 dimensions. Kuditipudi et al. (2019), LIT-671, proved that dropout-stable solutions are always joined, and constructed global minima that are not, so connectivity belongs to found solutions. Proposed: the evidence is pairs and small complexes of CIFAR classifiers. | Proposed |
| THEORY-110 v2 | A set of trained solutions has a centre that is linearly connected, after alignment, to the rest of them: the solution set is a star domain even where it is not convex | Sonthalia et al. (2024), LIT-659, conjecture that below the width at which SGD solutions become convex modulo permutation they are still a star domain, and train a star model whose barriers to held-out solutions, after weight matching, are about 2–5 times lower than those between solutions (ResNet-18 CIFAR-10 0.078 against 0.383; ImageNet 2.794 against 5.948), and not zero. Lin et al. (2024), LIT-682, prove star-shaped linear connectivity for wide two-layer teacher–student and deep linear networks, and find centres for five trained image classifiers with no permutation. Proposed: reduced, not zero, and no held-out test without alignment. | Proposed |
| THEORY-111 v3 | In image classifiers, between two networks linearly connected by spawning from a shared checkpoint or by permutation alignment (MLPs, and VGG-16, ResNet-20 and ResNet-50 on CIFAR-10 and Tiny-ImageNet), nearly every layer’s features at three points on the line were proportional to the interpolation of the endpoints’ features, and pairs that were not linearly connected were far from it | Zhou et al. (2023), LIT-674: whenever two image classifiers are linearly mode connected, by spawning or by permutation, the features of nearly every layer of the interpolated network are proportional to the interpolation of the endpoints’ features. This is layerwise linear feature connectivity, and two conditions, weak additivity of ReLU and a commutativity of weights with features, imply it exactly. Lubana et al.’s Lemma 2, LIT-669, gives the exact one-hidden-layer case: linear connectivity between interpolating minima forces shared activation patterns, and with shared patterns the hidden features are linear along the path. Measured on pairs at three interpolation points, image classification only. The regularity outside image classification, and the step to many-model averages such as soups and SWA, are QUESTION-318. | Active |
| THEORY-112 v2 | Aligning independently trained solutions over the architecture’s symmetries removed the linear barrier between them for MNIST MLPs and 32×-wide ResNet-20s on CIFAR-10, two-thirds of it for an ImageNet ResNet-50, and not all of it for VGG-16 or ResNet-20 at 1× width, the barrier after weight matching falling with width; for 6- to 8-layer ViTs and GPT-2s, permutations alone removed 63–90% of it, and adding an orthogonal map on the residual stream, learned against the loss at the path’s midpoint, took it to zero or near zero except on BookCorpus (0.42) | Entezari et al. (2022), LIT-652, conjectured that SGD solutions are one basin modulo permutation. Git Re-Basin (2023), LIT-661, aligned MNIST MLPs and 32×-wide ResNet-20s to zero barrier, but not 1×-width models or ImageNet ResNet-50. Ferbach et al. (2024), LIT-680, proved it for wide nets with independent neurons, with a width requirement exponential in the previous layer’s width. Theus et al. (2025), LIT-664, took transformers to zero only with an orthogonal map on the residual stream added; permutations alone left 0.29–1.60. Bo Zhao et al. (2025), LIT-655, place permutations inside the full symmetry group. Lubana et al.’s barriers between models that compute differently are the boundary. Whether most of the barrier goes at standard width on ImageNet or a language corpus under data-free alignment, and whether the barrier left rises with depth, is QUESTION-317. | Active |
| THEORY-113 v2 | Merging ResNets trained from different initialisations on disjoint halves of a label set by permuting one onto the other and averaging fell far short of the ensemble; their cross-model feature correlation fell with depth, merging only the early layers recovered most of the ensemble’s accuracy, and merging features within each model as well as across both helped at 4× width and above; Stoica et al. attribute the failure to features with no counterpart in the other model | Stoica et al. (2023), LIT-665, merge ResNets trained from different initialisations on disjoint label sets. Permute-then-average fails, which they explain by the permuted model lying in a basin for its own task only. Mean cross-model feature correlation falls with depth (0.50, 0.37, 0.27 at three depths). Merging only the early layers and keeping later layers as task heads recovers most of the ensemble’s accuracy. Merging features within one model as well as across both helps once the models are wide enough to hold redundant features. With full merging on ImageNet-1k, ZipIt! is no better than permutation (8.6%). No same-task control separates the effect of task difference from that of depth; that is QUESTION-316. | Active |
| THEORY-114 v2 | In image classification, linear mode connectivity appeared during training and not at initialization: copies of ResNet-20 and VGG-16 on CIFAR-10 and of ResNet-50 and Inception-v3 on ImageNet, trained from a shared state, became stable to SGD noise in test error only after 1.5–20% of training (LeNet on MNIST was stable from the start), and between independently initialized MLPs on MNIST and CIFAR-10 the barrier after weight-matching alignment was high at initialization and fell gradually through training | Frankle et al. (2020), LIT-654: two copies trained from step k under different SGD noise are linearly connected only once k is a little way in, at 1.5–3% of training for VGG-16 and ResNet-20 on CIFAR-10 and 16–20% for Inception-v3 and ResNet-50 on ImageNet. Git Re-Basin (2023), LIT-661: between independently trained MLPs, the barrier after permutation alignment is high at initialization and falls gradually over training. Entezari et al.’s theorem proves alignment-LMC at random initialization; Ferbach et al. (2024), LIT-680, show the width that needs grows recursively exponentially with depth, far past practical widths, which is why the two are consistent. | Active |
| THEORY-115 v2 | Linear connectivity from a shared, already-stable start holds only when the objectives the runs optimise share structure, and breaks as that structure is removed | Mirzadeh et al. (2020), LIT-651: from a task-1 solution, a model trained on tasks 1 and 2 together stays on a low task-1 loss line from the start, and one trained on task 2 alone does not. Adding noise to task 2’s inputs, corrupting its labels, or removing classes separates the solutions progressively. The authors explain it by curvature: the multitask direction avoids the earlier task’s top Hessian eigenvectors. Gueta et al. (2023), LIT-658: fine-tuning runs from one pretrained model are linearly connected within a dataset and a task family. Wen et al. (2023), LIT-681: in class-incremental learning the line between adjacent continual minima crosses a ridge in the old tasks’ loss. Limits: much of the measured breakage is forgetting at the endpoint, not a barrier, and FedAvg models from one random start under one global objective are separated by a barrier that grows with heterogeneity. | Proposed |
| THEORY-116 v2 | A linear barrier between two minima that survives the removal of symmetries marks a difference in the input attributes the two models rely on: they compute by different mechanisms | Lubana et al. (2022), LIT-669: models that rely on a synthetic cue and models that ignore it are separated by a linear barrier even after permutation matching. Fine-tuned models that keep a linear path to their parent keep its cue, and those that lose the path lose the cue. Their Conjecture 1 states this claim’s direction. What their Appendix F.3 proves, for a one-hidden-layer ReLU network with interpolating minima, is the converse: linear connectivity forces identical activation patterns, so models relying on attributes of different complexity cannot be linearly connected under any permutation. Zhou et al. (2023), LIT-674, support that converse in deep image classifiers, where linearly connected pairs have features that blend layer by layer. The stated direction rests on experiments with synthetic cues and on a one-layer sufficiency argument. | Proposed |
| THEORY-117 v3 | In Uselis, Dittadi and Oh’s two-concept grids, ResNet-50s trained from scratch, with checkpoints chosen on the unseen pairs, reach unseen combinations as the share of combinations seen grows and not as up to four times more data of the same combinations is added; and when embeddings are exactly linearly factored, seen pairs that connect every value of both concepts, as two per value arranged in one cycle do, determine the embedding of every unseen pair | Uselis, Dittadi & Oh (2025), LIT-667. In an n × n grid of two concepts with k combinations seen per value, ResNet-50s trained from scratch fit seen pairs and fail on unseen ones; four times the data of the same combinations leaves 60–80% drops, while more values and more combinations help. Features pass from spurious, to decodable but entangled, to linearly factored as coverage grows. Model selection was on the test set, by design, so the results bound what is possible. The record re-derived that exactly factored embeddings of every unseen pair are fixed by seen pairs connecting every value, as the paper’s k = 2 cycle does. Honest selection, other architectures and more concepts are QUESTION-207. | Active |
| THEORY-118 | Praiseworthiness is compatible with being psychologically determined by good reasons, but blameworthiness requires that the agent could have done otherwise, that is, could have acted on the right reasons | Susan Wolf’s asymmetry thesis, reported second-hand: the primary texts are unread. McKenna and Coates (LIT-291, §4.3), citing “Asymmetrical Freedom” and Freedom Within Reason pp. 79–81, report that for Wolf praiseworthy conduct does not require the freedom to do otherwise and blameworthy conduct does. An agent determined to act in accord with the True and the Good loses nothing by lacking the ability to act irrationally; an agent who acts against it and cannot act in accord with it cannot reasonably be blamed. In Fischer’s terms, only blame needs regulative control. Wolf holds that the ability needs only the falsity of psychological, not physical, determinism. | Proposed |
| THEORY-119 v2 | An agent can be morally responsible for what she did although she could not have done otherwise, when what made the action unavoidable played no part in bringing it about, so the principle of alternate possibilities is false | Frankfurt (1969, LIT-694, read): Black stands ready to make Jones4 act as he wants and never needs to, so Jones4 could not have done otherwise and is as responsible, for blame or praise, as without Black. A fact that plays no part in bringing an action about cannot excuse it. The 1971 willing addict (LIT-692, read) is a second route. Robb’s SEP entry (LIT-294) gives the standard objections: the dilemma defence from the prior sign, flickers of freedom, general abilities, and the case’s oddity. None is settled, and the record has read the replies only in survey. | Proposed |
| THEORY-120 | A motive is the agent’s own, and she acts of her own free will, when she identifies with it, and that is all the freedom moral responsibility requires: identification is the conformity of the effective desire to a decisive higher-order volition (1971), and later wholehearted acceptance with no conflict at any higher order | Frankfurt’s hierarchical, or endorsement, account, from his own texts: the 1971 paper (LIT-692, read) and the 2004 Tanner Lectures (LIT-293, read). A person’s will is the desire that moves him to act; he identifies with a desire by wanting it to be his will, decisively, and he acts of his own free will when the will that moves him is the will he wants. In 2004 the condition is “volitional unanimity” with no conflict “at any higher order”, and identification is “willing acceptance”, which may be resigned. Acting of one’s own free will is what responsibility requires, and alternatives and history are irrelevant. The 1987 and 1992 revisions are held only by report. | Proposed |
| THEORY-121 v4 | Moral responsibility requires guidance control, moderate reasons-responsiveness of the agent’s own actual-sequence mechanism, and not regulative control over alternative possibilities, so responsibility is compatible with causal determinism | Fischer and Ravizza, in their own précis (LIT-728, read): moral responsibility requires guidance control, not regulative control over alternatives. Guidance control is acting from a mechanism one has made one’s own by taking responsibility for it, which is moderately reasons-responsive: regularly receptive to reasons, some moral, and at least weakly reactive. Fischer’s 1987 paper (LIT-687, read) is the weak-responsiveness origin. The view is compatible with causal determinism. | Active |
| THEORY-122 | Moral responsibility requires the normative competence to recognise and act on the True and the Good, which identification with one’s own motives does not supply | Susan Wolf’s Reason View, reported second-hand: the primary texts are unread. McKenna and Coates (LIT-291, §4.3) report that for Wolf free will is the ability to act in accord with the True and the Good, an anchor outside the agent’s psychology. Talbert (LIT-691, §§3.1.1, 3.2) reports her case against deep-self or Real Self views and the JoJo case: JoJo identifies wholly with the cruel values his father raised him in, yet is not responsible, because he cannot appreciate that they are wrong. The claim is a necessary condition. It does not by itself say whether the ability must include being able to do otherwise; that is THEORY-118. | Proposed |
| THEORY-123 v2 | In ad hoc groups of students negotiating a bonus, a confederate’s randomly assigned pleasant or unpleasant mood spread to the other members, by their self-reports and by blind coders, and the more pleasant mood a group caught, the more cooperative and the less conflicted coders rated it, a correlation with measured contagion rather than a manipulated effect; members’ moods also converged without a confederate, and members did not credit their mood for how effective they judged themselves; the numbers are from the 2001 manuscript | Barsade (2002), LIT-706, read from the August 2001 manuscript, so every number is the manuscript’s. Study 1 (94 undergraduates, 29 groups): a confederate randomly assigned to show pleasant or unpleasant mood moved members’ self-reported mood by +.41 or −.26 (χ²(1) = 9.97), and blind video-coders rated members’ mood 2.75 against 2.33 (χ²(1) = 10.30). Members who caught more pleasant mood were rated more cooperative, and at group level coder-rated contagion correlated with cooperativeness (r = .44) and against conflict (r = −.42). Study 2 (113 MBA students, 26 groups, no confederate): the ICC of members’ mood rose from .00 to .24, and contagion correlated with members’ ratings of cooperation (.49) and conflict (−.49). Members related how pleasantly they behaved to others’ conduct but showed “absolutely no awareness” of mood bearing on their judged effectiveness. Valence and energy hypotheses failed or were marginal. Limits: one experiment, one actor, retrospective mood, correlational process effects. Promoted 2026-10-20 on what the manuscript measured (ADR-047 v3); the wider claim is THEORY-826. | Active |
| THEORY-124 v2 | In Posani et al.’s analysis of the IBL Brainwide Map, recorded while trained mice performed one visual decision task, the eight-variable selectivity profiles of neurons within one cortical area clustered beyond a covariance-matched Gaussian null only in VISp, AUDp and SSp-ul of about 20 areas tested, while profiles pooled across areas clustered along anatomical lines; and over the task conditions each area distinguishes, at least 95% of random balanced dichotomies were linearly decodable above a label-shuffled null in 15 of 16 areas, a lenient criterion | Posani et al. (2026), LIT-708: in about 14,000 cortical units of the IBL Brainwide Map, the 8-variable selectivity profiles of 4,617 selective neurons beat a covariance-matched Gaussian null for clustering within a region only in VISp, AUDp and SSp-ul. Elsewhere the profiles form an elongated, unclustered cloud. After merging conditions a region cannot tell apart (leaving 5 to 16 of 16), ≥ 95% of random balanced dichotomies are decodable above a shuffle null in 15 of 16 regions, GU being 0.82. Types do appear when regions are pooled, aligned with anatomy. One task, overtrained mice, a lenient separability criterion. | Active |
| THEORY-125 | A group can itself be in an emotional state that is not its members’ states in aggregation, when its distributed routines integrate the capacities an emotion requires into one action-oriented representation; because emotions are functional kinds such a state need not be felt, and no actual case has yet been shown | Huebner (2010), LIT-702: a genuinely collective emotion is a state of a group that “could not be exhaustively characterized in terms of intentional states of individuals in aggregation”. Fear requires danger detection, redeployment of attention, system-wide preparatory change and their coordination into one state with indicative content and imperative force; a distributed system can integrate routines that way. Some individual emotions are non-conscious, so a group’s need not be felt, and emotion kinds are functional (“like vodka”), so lacking homologous mechanisms does not exclude groups. The paper establishes a possibility, not an instance: its worked case, the USS Palau crew, turns out to be “collective detection of danger in the absence of a fear response”, and the replacement, the 2008 McCain–Palin campaign, is offered as “intuitively plausible” pending anthropological data. Proposed. | Proposed |
| THEORY-126 v2 | A collective emotion is the synchronous convergence of individuals’ affective responses to one event or object, produced bottom-up by shared appraisal, contagion and group membership, and it needs no group subject; it takes a We-mode form when the appraisals rest on collectively intentional states | von Scheve & Ismer (2013), LIT-696, a conceptual synthesis with no data: collective emotion is “synchronous convergence in affective responding across individuals towards a specific event or object”. Its minimal case is shared appraisal with no mutual awareness (drivers in one traffic jam). Mutual awareness and membership in a collective amplify it, and appraisals grounded in collective intentions give “We-mode” collective emotion, which they expect to differ in quality. Barsade (2002), LIT-706, supplies the one measured instance: in 26 groups with no confederate, the intraclass correlation of members’ mood rose from .00 to .24. The account posits no group subject and does not deny one. Proposed: the definition is stipulated, the routes beyond contagion are untested, and the We-mode clause is a hypothesis its authors say lacks evidence. | Proposed |
| THEORY-127 v4 | On the court agenda, and on any agenda in which every proposition reaches every other by conditional entailment and some minimally inconsistent triple stays consistent with two of its members negated, a group whose judgments are robustly rational under universal domain and respect unanimity cannot form its judgment on each proposition from its members’ judgments on that proposition alone unless one member dictates; its judgments must supervene on the members’ whole sets of judgments, and so can depart from what the members judge on the same proposition while being wholly fixed by them | List & Pettit (2006), LIT-705: under universal domain, robust group rationality (complete, consistent, deductively closed group judgments for every profile of rational member judgments) is inconsistent with majoritarian, uniform proposition-wise and proposition-wise supervenience (Propositions 1–3; the last two proved elsewhere and cited), and consistent with set-wise supervenience, which the premise-based and distributed premise-based procedures achieve (Propositions 4–5). Members’ judgments on a conclusion can then be insufficient, or even unnecessary, to fix the group’s judgment on it. List (2014), LIT-700, makes this the mark of a third kind of collective attitude: corporate attitudes, a group agent’s, supervene “holistically”, while aggregate and common attitudes supervene proposition by proposition. Active since 2026-10-19 for categorical judgments on the court agenda and on agendas with two stated connectedness conditions: the record re-derived Proposition 3 (and Proposition 2 as a corollary) itself. The extension to corporate attitudes in general is QUESTION-152. | Active |
| THEORY-128 | After mass bleaching, coral recovery on a reef crest depends on large herbivorous fishes keeping macroalgae down, because recovery runs through recruitment and survival that macroalgae suppress, not through the persistence of surviving colonies alone | Hughes et al. (2007), LIT-711. On the reef crest at Orpheus Island after the 1998 bleaching, four roofless cages kept large and medium fishes out of 25 m² plots for 30 months. Macroalgae averaged 56% cover inside against 4.1% and 1.7% in controls. Coral cover reached 7.7% inside against 19.2% and 20.2%, with recruitment about two-thirds lower and mortality of established colonies more than double. Control recovery came mainly from recruits of taxa bleaching had removed. Proposed: one site, four replicates, plot scale, and fish exclusion standing in for herbivore exclusion. The algal state vanished within 30 days of reopening. | Proposed |
| THEORY-129 | In Acropora millepora the natural night-light regime is necessary for spawning on the expected night, and displacing it delays or abolishes both release and a spawning-night programme of G-protein-coupled signalling genes | Kaniewska et al. (2015), LIT-710, at Heron Island. In 2011, colonies under natural night light spawned with the reef, while colonies lit after sunset or kept dark for the preceding week did not spawn that night (N = 6, 5, 5). 184 transcripts changed around release in ambient colonies, early in lit ones and not at all in dark ones, and the induced genes were enriched for G-protein-coupled signalling. In 2006, blue, green or white nocturnal light delayed spawning 6–8 h or two nights and red did not. Proposed: one species and site, small groups, and a cascade inferred from co-expression. It shows synchrony by a shared cue, not coupling between colonies. | Proposed |
| THEORY-130 | Coral bleaching is the breakdown of a regulated host–symbiont exchange, reached by more than one route, not a single mechanism of symbiont loss | Two reviews, with no data of their own. Boilard et al. (2020), LIT-712, collect the regulators of the coral–dinoflagellate exchange: the host controls symbiont density, bacteria shift the nitrogen supply, and heat leads either to host rejection of symbionts (apoptosis, autophagy, exocytosis, detachment, necrosis) or to pigment loss under oxidative stress. Goulet et al. (2020), LIT-709, report two octocorals whose similar symbiont losses at +3 °C came by different routes, one by fewer symbionts per host cell and one by loss of host cells. Proposed. The claim that the wider microbiome drives bleaching is declined: its own source says it cannot yet be tested. | Proposed |
| THEORY-131 v2 | A corporation whose Corporate Internal Decision (CID) Structure, an organizational chart of stations plus recognition rules embedded in corporate policy, licenses redescribing its members’ acts as done for corporate reasons is a non-eliminable intentional agent, unlike a mob; and if intentional agency suffices for moral personhood, which French asserts but here says he cannot further argue, such a corporation is a full-fledged moral person | French (1979), LIT-727. Moral persons are non-eliminable subjects of accountability, so intentional agents. A corporation’s CID Structure licenses redescribing members’ acts as corporate acts, and an act that implements established corporate policy is done for corporate reasons. Proposed: the step from agency to moral personhood is asserted, and corporate intentionality is shown by licensed redescription, not by any test. | Proposed |
| THEORY-132 | Stability, a system’s speed of return to equilibrium after disturbance, and resilience, its capacity to absorb change and persist within its domain of attraction, are distinct properties that can trade off, so a system can be highly unstable and highly resilient, and managing it for constancy can erode its resilience | Holling (1973), LIT-741. Stability is return to equilibrium. Resilience is persistence under change, set by the extent of the domain of attraction and the system’s distance from its edge. Budworm forests and insect populations in harsh climates are unstable and resilient; homogeneous lakes are stable and fragile. Active for the distinction, which has become standard. The claim that management for constancy erodes resilience rests on suggestive cases. | Active |
| THEORY-133 v2 | In List and Menzies’s account of causes as difference-makers, a higher-level property that makes a difference to an effect is its cause, and its realizer is not, exactly when in some nearest situation without that realizer the property is realized differently and the effect still occurs; which holds depends on each causal system’s counterfactual structure, not on levels a priori | List & Menzies (2009), LIT-722. Take causes to be difference-makers. Then Kim’s exclusion principle fails, and a revised one holds or fails system by system. Given that a higher-level property makes a difference to an effect, its realizer is not a cause exactly when some nearest situation without the realizer has the property realized otherwise and the effect present; the record re-derived this. The claim that higher-level relations are typically insensitive to their realizers is an observation about scientific practice, and Pernu disputes the paper’s main example. Which systems meet the condition is QUESTION-213. | Active |
| THEORY-134 v2 | Whether a system can persist is a question about a constraint set fixed independently of its dynamics: a set is viable when from each of its states some evolution can stay in it, and when it is not, its viability kernel is the largest part that is, from the rest of which every evolution leaves in finite time | Aubin’s viability theory, read in his 1999 mini-course notes LIT-714. Given dynamics and a set K of required states, K is viable if some evolution from each state stays in K and invariant if every one does. Nagumo’s theorem reduces viability to a tangency condition. The viability kernel is the largest viable subset of K; from outside it every evolution exits K. The notes do not compare viability with stability; that contrast is a further step. | Active |
| THEORY-135 v2 | Multicellular cooperation depends on suppressing cells that gain fitness at the expense of the organism, across five foundations (proliferation inhibition, controlled cell death, division of labour, resource allocation and maintenance of the extracellular environment); cancer-like cheating on them is found across the independent origins of complex multicellularity, so complex multicellularity can be understood as a system for detecting and suppressing cheaters | Aktipis et al. (2015), LIT-740. Multicellularity requires cell-level fitness to be suppressed; cancer is cheating on five foundations of cellular cooperation. A survey of the independent origins of complex multicellularity finds cancer-like cheating widely, division-of-labour cheating in every form. Proposed: a literature review whose survey is limited by what has been studied, with no model or new data. | Proposed |
| THEORY-136 v3 | A persistent or abrupt change is not evidence that a system has alternative stable states: field patterns such as jumps, multimodality and dual relationships also arise from a stepwise driver or a simple threshold, and only hysteresis, initial-state dependence or a lasting shift after a temporary disturbance, with slow return excluded, comes close to showing one | Scheffer & Carpenter (2003), LIT-726. Alternative attractors predict sudden shifts, multimodal states and dual responses to a driver, and so do discontinuous drivers and threshold responses. Discriminating evidence is experimental: different starting states reaching different end states, temporary disturbances causing lasting shifts, or hysteresis. Slow recovery can mimic all three. Positive feedback must be strong to produce alternative states. Active as a methodological standard. | Active |
| THEORY-137 v2 | Attributions of mental states to institutions, such as the knowledge that the collective knowledge doctrine of corporate criminal law attributes to a corporation no member of which held it, work largely by shaping the institutions to which they are made rather than by describing states they already had: the attribution holds the institution to a norm, the institution builds structures to meet it, and it becomes more predictable from the intentional stance, whether or not institutions really have minds | Tollefsen (2025), LIT-736. Both sides of the group-mind debate treat ascription as tracking pre-existing causes. On the regulative view of folk psychology it shapes its target. In United States v. Bank of New England a court held a bank to know what no employee knew, and banks then built systems to detect reportable deposits. Narratives regulate too. Proposed: the regulative view is assumed, and the effect on banks is asserted, not documented. | Proposed |
| THEORY-138 | X is a cause of Y exactly when some intervention on X with respect to Y would change Y, where an intervention is an exogenous causal process that alone sets X (M1), affects Y only through X (M2), is not caused by anything that affects Y by another route (M3), and leaves Y’s causes off the path through X unchanged (M4); so defined, causation is not reduced to non-causal facts but is not viciously circular, and needs no human agent | Woodward, “Causation and Manipulability” (SEP, 2001; revised 2023), LIT-713. A cause is what changes the effect under a surgical, exogenous intervention, defined relative to the effect by M1–M4. The account separates total from direct causes by combining interventions, and treats natural experiments as interventions. Active as the standard the record uses for what a causal claim asserts. This statement says nothing about invariance, proportionality or levels. | Active |
| THEORY-139 v4 | A corporation that forms its judgments through authorised avowal and corrects the inconsistency any mechanical aggregation of its members’ views produces has a mind of its own, and as a conversable agent it meets the conditions for being fit to be held responsible: a significant choice, the capacity to judge its options normatively, and control over acting on that judgment | Pettit (2017), LIT-718, restating Responsibility Incorporated (2007). Corporations are conversable agents: spokespersons avow and commit in their name, and because majority aggregation can be inconsistent they must form their own minds. Conversable agents are fit to be held responsible under three conditions, which corporations meet. Proposed: it is an argument, and its empirical premise about corporate procedure is asserted rather than shown. | Proposed |
| THEORY-140 v2 | The Columbia Accident Investigation Board found that the institutional causes of the Challenger accident had not been fixed and recurred in Columbia’s: in both, evidence that the design was not performing as expected was repeatedly reinterpreted as acceptable, each decision seeming correct in itself and each survived anomaly justifying the next flight, while budget and schedule pressure, consensus sign-off, a hierarchy that kept dissent from rising and a safety organization dependent on the program it oversaw sustained the pattern for twenty years and undid post-Challenger reforms | Columbia Accident Investigation Board (2003), LIT-734, applying Vaughan’s normalization of deviance (LIT-715, unread). Foam strikes and O-ring erosion followed the same trajectory of incremental acceptance. Organizational culture, structure and political constraint reproduced it, so “history is cause”. Two cases in one agency, reconstructed after the fact. The title states the Board’s finding; whether the pattern is general and causal, which is Vaughan’s theory in a book the record has not read, is QUESTION-334. | Active |
| THEORY-141 v2 | In a major evolutionary transition, where formerly free-living units come to form a higher-level unit, the collective is stable only if selection between collectives comes to trump selection among the units within them, typically through mechanisms such as policing, kinship and division of labour that align the interests of the units; the levels at which selection acts are then a product of evolution, to be explained rather than assumed | Okasha (2022), LIT-749, restating with Buss and Michod a principle of the major transitions: a new collective can be undone by defectors, and succeeds only if higher-level selection trumps lower-level selection, usually through policing or aligned interests. The transitions make the hierarchy an explanandum. Proposed: a review stating general principles that Okasha himself says may explain any one transition only coarsely. | Proposed |
| THEORY-142 | Because the returns to exploitation are surer, nearer and closer to the decision than the returns to exploration, organizational learning refines exploitation faster and tends to become self-destructive in the long run; and where an organizational code learns only from members who deviate from it, slow socialization, a mix of slow and fast learners and moderate turnover raise what the organization knows, while without turnover a changing environment degrades its knowledge to chance | March (1991), LIT-729. Exploration’s uncertain, distant returns lose out to exploitation’s under learning from experience, trapping organizations in suboptimal equilibria. In a simulation of mutual learning between members and a code, deviation is the code’s only source of improvement, so fast socialization hurts the organization and moderate turnover helps it. Proposed: the dynamics are shown only in a stylized model, and the trade-off is argued, not measured. | Proposed |
| THEORY-143 v3 | When a group learns only about the options its members pursue and good evidence is scarce, sparser communication makes it more likely to settle on the better option, at a large cost in speed; when evidence is plentiful, sparsity only slows learning | Zollman (2007), LIT-724, simulated Bala and Goyal’s bandit model: cycles chose the better method more often than complete graphs, and more slowly; density, not centrality, predicted failure. Rosenstock et al. (2017), LIT-733, found the effect only where inquiry is hard: close alternatives, small groups, small batches. Proposed: all of it is simulation, and real communities’ place in parameter space is unknown. | Proposed |
| THEORY-144 | Under steady cost and effort pressure, an organization’s activity migrates toward the boundary of acceptable performance, and redundant defences erode unobserved because a breach of one shows no effect, so that major accidents arise from many locally reasonable decisions rather than from coincident errors | Rasmussen (1997), LIT-743. Within a work space bounded by functional, administrative and safety constraints, a cost gradient from management and an effort gradient from the work drive activity toward the boundary. Defence in depth hides the drift, and accidents such as Zeebrügge are prepared by decision makers each optimising locally. Proposed: the account is built from accident reconstructions, which see only the cases that crossed. | Proposed |
| THEORY-145 | Organizations that espouse revising their governing values characteristically fail to, because the theory-in-use people actually act on keeps premises tacit and tests self-sealing, and the resulting defensive routines make the inconsistency, and its undiscussability, undiscussable; so errors are corrected within the governing values (single-loop) while the values themselves go unexamined | Argyris (2002), LIT-745. Single-loop learning corrects errors within governing values; double-loop learning changes them. People espouse the second but act on Model I (control, winning, suppressing negative feelings, appearing rational). Defensive routines then make the gap undiscussable, and individual and organizational routines reinforce each other. Proposed: the evidence is the author’s own workshops, and the universality claim is asserted from earlier work. | Proposed |
| THEORY-146 v2 | In Holman and Bruner’s bandit model of honest Bayesian researchers whose beliefs funding cannot touch, who differ in method and whose influence and training of newcomers follow productivity, industry funding of those whose methods already favour its drug lowers, in the runs their figures report, the share of the community on the better treatment, and has no effect without methodological diversity; at the one setting reported, an independent funder that counts industry-funded trials toward its merit threshold lowers that share further, and one that excludes them raises it | Holman & Bruner (2017), LIT-744. In a Zollman bandit model with methodological diversity, productivity-weighted influence and turnover, industry funding of agents whose methods favour the drug lowers the chance of converging on the better action, though no agent’s beliefs respond to funding. A merit-based independent funder worsens it; one ignoring industry-funded trials counters it. Held as what the model shows; whether real fields work this way is QUESTION-315. | Active |
| THEORY-147 | Deep responsibility is not limited to the moral, and attributability and accountability are independent kinds of it rather than two levels: accountability needs only that the agent acted as she ought not to, was in a position to know it, and that acting so was up to her, while what makes a self a fit target of the reactive attitudes is plausibly that it can perceive, understand and appreciate the world as we do | Wolf (2015), LIT-747, the 2013 Routledge Lecture. We are deeply, not merely causally, responsible for nonmoral traits and art, by the self-disclosure view. Watson’s two-level view, accountability as attributability plus control, is rejected: a stipulated psychopath may be accountable for acts whose source is not attributable to him. Fitness for reactive attitudes is, on Wolf’s hunch, being an intelligent self. Proposed: the positive view is her hunch. | Proposed |
| THEORY-148 | A group learning by trying needs diversity in what its members pursue that lasts long enough to survive misleading early evidence and then gives way to consensus; limited communication and stubborn priors each supply it, and together they make it permanent, so the group never settles | Zollman (2010), LIT-735: in a bandit model with beta priors, sparse networks and extreme priors each maintain diversity of pursuit and each improve reliability, but combined they keep diversity alive so long that agents fail to converge. Rosenstock et al. LIT-733 find this the result that is robust across the models they test. Proposed: shown only in simulation. | Proposed |
| THEORY-149 | Users can govern a shared resource durably without either privatisation or central control, and the institutions that last are marked not by particular rules but by structural regularities: user-made and user-monitored rules, graduated sanctions, cheap local conflict resolution, recognised rights to self-organise, and nested layers of governance | Ostrom’s account, read in her Nobel lecture (LIT-719). Coded case meta-analyses, laboratory and field experiments and multi-country field studies agree that resource users often self-govern successfully. Long-surviving institutions share eight design principles that failed ones lack. The principles are correlates of survival, not tested causes, and their reach beyond common-pool resources is not shown. | Active |
| THEORY-150 | A platform that sits between the two sides of a market and can cheaply change how it allocates value tends to decay in three stages, first good to its users, then abusing them to favour its business customers, then abusing both to claw the value back for itself, each stage made possible by the lock-in the one before it built; how far it can go is set by the cost of leaving, so lowering that cost is the remedy | Doctorow’s enshittification, as he states it in the 2023 essay that named it, LIT-731. Platforms hand surplus to users, then to business customers once users are locked in, then to shareholders once both are; blocked interoperability and monopoly widen what users will bear. The remedy is end-to-end delivery and freedom of exit. Proposed: an essayistic thesis argued from cases, not a study. | Proposed |
| THEORY-151 v2 | Scientific objectivity belongs to a community’s critical practices rather than to individual method: because evidence bears on hypotheses only through background assumptions that no evidence supports, a community is objective to the degree that its criticism has venues, uptake, public standards and tempered equality of intellectual authority | Longino’s critical contextual empiricism, as she states it in the SEP (LIT-725). Underdetermination leaves background assumptions that only community criticism can check. Criticism confers objectivity only if it meets four norms: venues, uptake, public standards, and tempered equality. Proposed because the record reads the summary, not the books, and the norms’ epistemic benefit is argued rather than shown. | Proposed |
| THEORY-152 | When a firm, public service or other organization deteriorates, its members’ exit and voice are both recuperation mechanisms: voice carries richer information than exit and can be felt as a benefit rather than a cost, exit can be costly even without loyalty and can signal nothing, loyalty makes members voice rather than exit, and an organization needs floor levels of both for feedback but disintegrates or is disrupted beyond ceiling levels, while its managers may favour whichever response least threatens their hold on power | Hirschman (1974; Milbank reprint 1980), LIT-750, revisiting his 1970 book (LIT-748, unread). Exit and voice are the two ways members respond to decline and the two channels of feedback. Voice deserves more weight than the book gave it; exit is neither free nor always informative; managers manage both. Proposed: argued from examples, and loyalty’s role is presupposed from the book rather than developed. | Proposed |
| THEORY-153 | A system can keep its identity independently within a shared environment only if it has five interacting subsystems, the first made of elements that are themselves viable systems, so that the structure recurs at every level of recursion; when one is missing or fails, the system degrades in characteristic ways, and without the subsystem for foresight the subsystems for operational control and for identity collapse into each other, leaving a system that can only react | Beer’s Viable System Model, as he states it in his 1984 retrospective LIT-752. Five subsystems are necessary and sufficient for any organism or organization to maintain its identity independently; every viable system contains and is contained in one; breakdowns trace to a failing subsystem. Proposed: the paper declines to validate the model, the evidence is the author’s consultancy, and no observation the model forbids is named. | Proposed |
| THEORY-154 | Whether an expected tangible reward lowers or raises later intrinsic motivation depends on how tightly its stated contingency ties it to performance and success | Cameron, Banko and Pierce (2001, LIT-562), re-analysing 145 studies with contingencies coded by procedure. On interesting tasks, expected tangible rewards undermine later free choice when loosely tied to performance (for doing the task, for “doing well”) or earned at less than the maximum; they do not when given for surpassing a score, and they enhance it when given for exceeding others. Read through social cognitive and behavioural theory: rewards tied to success carry competence. Proposed: the paper measures no mediator and pools control groups that differ in feedback. | Proposed |
| THEORY-155 v2 | Iterated learning by Bayesian agents who sample from the posterior converges, in an ergodic chain, to the shared prior | Griffiths & Kalish (2007), LIT-769, read in NOTE-599: a chain of learners who share a prior and each sample a hypothesis from their posterior is a Gibbs sampler, so the probability a learner holds a hypothesis converges to its prior probability, whatever the amount of data passed on; with MAP learners the outcome centres on the prior’s mode but depends on data amount and noise, and can amplify weak biases. It is a theorem about an idealized chain. It does not say human chains reach the prior, and Kirby, Cornish & Smith’s laboratory chains, LIT-771, are consistent with it without testing it. Whether human chains do is QUESTION-137. | Active |
| THEORY-156 v3 | For experiments on a finite parameter set whose outcome spaces are standard Borel, being at least as informative for every decision problem is the same as being able to simulate the other by a randomisation | Blackwell (1953), LIT-781, Theorem 8 with Theorems 1–3: for experiments with finitely many states and decision problems with bounded losses, α attains every loss vector β attains, in every problem, exactly when a Markov kernel turns α’s observation into β’s under every state. The direction from simulation to informativeness is Blackwell (1951); the finite converse is Sherman and Stein (1951); the general converse is proved in 1953. It is a qualitative order and says nothing about how much worse an incomparable experiment is. The record re-derived the converse for standard Borel outcome spaces (note of 2026-10-29); arbitrary spaces, which the paper claims through a quoted 1951 result, are QUESTION-321. | Active |
| THEORY-157 | The classical theorems on sufficient statistics need only the copy/discard structure of Markov kernels: Basu’s theorem holds in every Markov category, and Fisher–Neyman and Bahadur need only strict positivity, not the existence of conditional distributions | Fritz (2020), LIT-772, read in NOTE-588, Theorems 14.5, 15.8 and 16.3 with the definitions of Sections 13–15. Sufficiency, completeness and ancillarity are stated with copy, discard, composition and almost-sure equality alone. Basu’s theorem follows with no further axiom; Fisher–Neyman and Bahadur use strict positivity, which Stoch has although it lacks regular conditionals. The match with the classical theorems is shown in FinStoch (Fisher–Neyman) and through bounded completeness in Stoch (Basu), not for measure-theoretic Fisher–Neyman. | Proposed |
| THEORY-158 v2 | For a Markov process on a finite state space, an observable commutes with the generator exactly when its mean and variance are both conserved in every state, which is exactly when it is constant on each connected component of the transition graph, so a conserved mean alone does not give a symmetry | Baez & Fong (2013), LIT-773, read in NOTE-598: Theorem 1 (finite state space, four equivalent conditions), which the record re-derived. Theorems 2–3 (σ-finite measure spaces, without the component form) are reported as the source’s (QUESTION-144). Unlike quantum mechanics, where a mean conserved in every state already implies commutation, a Markov process can conserve the mean of an observable it does not commute with. The theorem covers diagonal observables only; it says nothing about symmetries that permute states. | Active |
| THEORY-159 | In a language a term’s value is fixed by its relations to the coexisting terms of the same system, so terms that share a signification can differ in value | Saussure (1916), LIT-774, read in NOTE-594, Part Two ch. IV. Value, the horizontal relation among signs, is distinguished from signification, the link inside one sign; the concept side and the sound side of a term are each “purely differential”. It does not say that the sign as a whole is nothing but a difference: the book calls the sign a positive fact and the relation between signs opposition. The support is argument by example. | Proposed |
| THEORY-160 v2 | In the algebraic Hamiltonian setting, symmetry and conservation correspond because the bracket is antisymmetric, which for a bilinear bracket is each observable conserving itself; the theorem’s content lies in identifying observables with generators | Baez (2020), LIT-819, read in NOTE-630, Theorems 3, 4, 8 and 10, with Alfsen and Shultz’s theorem quoted as Theorem 12 and not checked here (QUESTION-142). With unique solutions to the flow equations, “a generates symmetries of b iff b generates symmetries of a” is {a, b} = 0 ⇔ {b, a} = 0. It assumes reversible one-parameter groups and an observable–generator map; it says nothing about dissipative or stochastic dynamics, nor about the Lagrangian form of Noether’s theorem. | Active |
| THEORY-161 v2 | In Zhao et al.’s (2025) and Chai et al.’s (2023) semantic rate–distortion frameworks, meaning is a latent variable with a known joint law with the observation, so their limits are indirect source-coding limits; Zhao et al.’s posterior-matching semantic distortion is, with KL divergence, exactly the information bottleneck, and with total variation a bound on the expected lost value of every bounded-loss decision | From the readings of Zhao et al. (2025), LIT-793, Chai et al. (2023), LIT-812, and the survey of Xin, Fan and Letaief (2024), LIT-823. These frameworks fix meaning as a hidden S with a known p(S, X); their theorems are indirect rate–distortion results that do not depend on what S is. Zhao et al.’s posterior distortion reduces, for KL, to I(S;X) − I(S;Y), making the function the information bottleneck (LIT-338), and for TV bounds the extra Bayes risk of every bounded loss. The two identities are this record’s derivations, not the papers’. | Active |
| THEORY-162 | What an utterance does to the context it is used in is part of its meaning, and its truth conditions do not fix it: sentences with the same truth conditions can differ in what they make available to later discourse, in whether they inform or only test, and in whether they describe a state of affairs or bring one about | Heim (1982), LIT-838; Veltman (1996), LIT-818; Krifka (2024), LIT-835. Three readings find, each in its own domain, sentences that agree in truth conditions or in the proposition they carry but differ in their effect on a conversational state. The effects are anaphoric potential (Heim), tests rather than information (Veltman), and changing indices rather than eliminating them (Krifka). This is the dynamic view: meaning as context-change potential. It does not say that truth conditions are irrelevant, since each framework recovers them, or that the three formalisms agree with each other. | Proposed |
| THEORY-163 v3 | In Zaslavsky, Kemp, Regier and Tishby’s analysis, the colour-naming systems of the World Color Survey languages and English lie near the information-bottleneck bound for compressing perceptual meanings into words, at a trade-off parameter just above 1 and nearer than hue-rotated variants of themselves, with the need distribution over meanings estimated from the naming data | Zaslavsky, Kemp, Regier & Tishby (2018), LIT-810, read in NOTE-631: treating a colour lexicon as an encoder from Gaussian perceptual meanings to words, the World Color Survey languages and English lie near the IB curve of LIT-338 at β ≈ 1.03, beat hue-rotated variants of themselves, and their soft, partly inconsistent naming is what IB optima look like. It does not show that languages are driven to the bound by any process, and the need distribution that makes the fit best is estimated from the naming data themselves. | Active |
| THEORY-164 v3 | As Raviv, Meyer and Lev-Ari report it, in a laboratory game where 12 fully connected groups of eight and 12 of four built a new communication system with total interaction held fixed, the larger groups’ languages grew more systematic faster, ended more systematic and differed less from one another, while communicative success and convergence did not differ by size; input variability, higher in the larger groups, predicted the next round’s gain in structure, an association measured and not manipulated | Raviv, Meyer & Lev-Ari (2019), LIT-825, read in NOTE-628: fully connected groups of eight built more systematic languages than groups of four, faster and more uniformly, with total interaction and network structure fixed; input variability, larger in bigger groups, predicted the gains. One laboratory study, two group sizes, and a mechanism supported by lagged association, not manipulation. It says nothing yet about natural communities, where size travels with network density and second-language learners. | Active |
| THEORY-165 v2 | Within a fixed measurement scenario, the non-contextual fraction is the value of a linear programme whose constraint vector is the empirical model’s probability table, and the contextual fraction is convex under mixing | From Abramsky, Barbosa & Mansfield (2017), LIT-265: the non-contextual fraction is the value of a linear programme whose constraint vector is the empirical model (Eq. 3), and convexity of CF under mixing is their Theorem 2. Piecewise linearity and the Lipschitz bound are the record’s own derivation, now CLAIM-372. The Lipschitz constant depends on the scenario and is not bounded here. Nothing here applies to signalling data, where CF is undefined. | Active |
| THEORY-166 v3 | In the 66 Pew surveys of 2001–2011 that varied the order of two back-to-back binary questions, question order changed the answers but not the probability of giving the same answer to both, the equality a Lüders projection model predicts for any projectors; a classical model with order events can meet the same equality, so the regularity does not by itself favour quantum over classical probability | Wang, Solloway, Shiffrin & Busemeyer (2014), LIT-795, on the QQ equality derived in LIT-834: across the 66 Pew surveys of 2001-2011 that varied the order of two questions, question order shifts the answers (p = 0.0004) but not the probability that the two answers agree (p = 0.4625). The Lüders projection model predicts this without parameters, by a one-line identity. A classical model with order events can be built to satisfy the equality, and LIT-264 shows that data meeting it are noncontextual, so it is evidence for a constraint on order effects, not for nonclassical probability or contextuality. A preregistered test with a constrained classical rival is QUESTION-210. | Active |
| THEORY-167 v3 | The Russian wondertale is built from a small fixed set of character functions in a fixed order, so that all wondertales share one composition and differ in who performs the functions and how | Propp (1928), LIT-828, read in NOTE-615: in Afanasyev’s tales 50–151 the constant elements are 31 functions of characters, defined by their consequence for the action, occurring in one order and falling to seven roles. One analyst, one corpus of a hundred tales, and a class of “wondertales” redefined in the end as the tales that follow the scheme. It does not say all folktales, or all narratives, share the structure, and the claims of a single source tale and of mythic origin are conjectures the book does not support. | Proposed |
| THEORY-168 v3 | In Contextuality-by-Default, whether a fixed set of measurements is contextual depends on how the system is represented: which couplings are imposed, and which dichotomizations of the variables are included | Dzhafarov, Cervantes & Kujala (2017), LIT-790, with Dzhafarov & Kujala’s CbD 2.0 (LIT-831) and CbD 1.0 (LIT-777). The same measurements can receive different verdicts. Maximal and multimaximal couplings can disagree when a content appears in three or more contexts (four, for binary variables), and the record’s worked case shows it. Multimaximal couplings of non-binary variables can be destroyed by coarse-graining. With every dichotomization kept, two content-sharing variables are contextual on their own unless one nominally dominates the other. The authors present the representation as the analyst’s choice, not as a defect. What the record does not get from these papers is any rule for choosing it. | Active |
| THEORY-169 v2 | For unnormalized causal linear attention and for softmax attention, conditioning on a context is exactly training a learner on it and predicting: the first is one batch gradient step of a linear inner model from zero, the second kernel regression that stores the context, and one linear self-attention layer with constructed weights carries one gradient step of in-context linear regression; for these layers conditioning and per-sequence weight updates differ in what state is kept, not in kind | Sun et al. (2024), LIT-801, Theorems 1–2, with von Oswald et al. (2022), LIT-792, Proposition 1. Linear attention equals a layer whose state is a linear model’s weights, updated by batch gradient descent on the context from zero; softmax attention equals a Nadaraya–Watson learner whose “training” appends the context to a list; and, with constructed weights, one linear attention layer reproduces one gradient step of a linear regression on in-context pairs. These are identities of output for specific layers. They do not say that trained transformers do gradient descent (the anthology rejects that, ANTH-THEORY-068), nor anything about weight updates that persist across sequences. | Active |
| THEORY-170 v2 | Languages differ in what their grammar obliges a speaker to convey rather than in what they can convey, so interlingual translation must add some information and leave some unexpressed, and repeated translation can erode a message | Jakobson (1959), LIT-786, after Boas: every cognitive content can be expressed in any language, but each grammar obliges its speakers to answer certain questions (aspect, number, gender, tense, definiteness). Translating between grammars that ask different questions forces the translator to supply answers the source did not give and to leave unexpressed answers it did, and a chain of translations of an isolated sentence can lose its content, less so the richer the context. Argued from examples, not tested; it concerns cognitive content, not pragmatic force. | Proposed |
| THEORY-171 v3 | When the causal constraints on events depend on context, deterministic assignments that are causal in each context can fail to glue into one causal assignment, so causal structure is itself a source of contextuality | From Gogioso & Pinzani’s trilogy: The Topology of Causality, LIT-808, read in NOTE-612, with the definitions of The Combinatorics of Causality, LIT-800 (NOTE-635). Over a space of input histories with the lowerset topology, causal functions form a separated presheaf, and on the space Θ₃ it is not a sheaf: two causal assignments on disjoint opens give one event two outputs on their common extension. That example was checked here, and it settles the claim. The source’s Theorem 2.34, that the presheaf is a sheaf exactly when no two contexts impose incompatible causal pasts on a common event, is reported as the source’s. Its proof was not read, and it is QUESTION-143. It does not say any physical or quantum data display the effect. | Active |
| THEORY-172 v4 | In Frank and Goodman’s one-shot reference games, listeners’ mean bets matched a parameter-free listener inverting a speaker who chooses among true utterances by informativeness, with a separately measured salience prior, and not salience alone; and in Bergen, Goodman and Levy’s signalling games with novel symbols, listeners read a signal as excluding what the available alternative would have conveyed | Frank & Goodman (2012), LIT-821, read in NOTE-634: a parameter-free Bayesian listener inverting a size-principle speaker, with a separately measured salience prior, matches mean listener bets over seven context types at r = .99 (.87 without the 0 and 100 predictions), while salience alone correlates at r = .19. Bergen, Goodman & Levy (2012), LIT-809, read in NOTE-613: with novel signals and no conventions, listeners read the signal as the object its alternative did not name, and lexical uncertainty derives Horn’s mapping. Goodman & Frank (2016), LIT-816, states the framework. Shown for artificial games with given alternatives, by fits of condition means with no rival fitted; a test against named rivals on trial-level data is QUESTION-209. | Active |
| THEORY-173 v2 | Large models are a cultural and social technology rather than agents: lossy, uninvertible summaries of human-produced information that, like prices and bureaucratic categories, let it be reorganized at scale | Farrell, Gopnik, Shalizi & Evans (2025), LIT-848, read in NOTE-649. A classification argued by analogy with print, markets, bureaucracies and elections, with one mechanism (fit to the average makes models worst on rare cases, which may homogenize culture). Proposed: no evidence is offered, and the paper gives no criterion by which the classification could fail. | Proposed |
| THEORY-174 v3 | Classical simulations between no-signalling empirical models on different scenarios never create contextuality, and a convex map between two scenarios’ model sets is induced by a classical non-adaptive procedure exactly when some non-contextual model of the hom scenario that satisfies its predicate induces it | Karvonen (2018), LIT-846; Abramsky, Barbosa, Karvonen & Mansfield (2019), LIT-847; Barbosa, Karvonen & Mansfield (2021, v2 2024), LIT-845. A simulation answers each measurement of the target by a jointly measurable set of the source’s, with shared classical randomness, so the cover may change. Along any simulation the non-contextual fraction cannot fall; contextual models cannot be cloned; and which maps between model sets are classical non-adaptive procedures is a non-contextuality question on a hom scenario, re-derived here. No-signalling models only, and nothing about information preserved. | Active |
| THEORY-175 v3 | Cosine similarities to matched anchor points are unchanged by exactly the maps that preserve each sample’s cosines to the anchors, among them every orthogonal map times a positive scalar and every per-sample positive rescaling but not translations; in Moschella et al.’s experiments independently trained encoders agreed in them only approximately, enough for a decoder reading them to transfer untrained between seeds, architectures and languages with loss, while their nearest neighbours mostly differed | Moschella et al. (2022; ICLR 2023), LIT-849, as read in NOTE-652. The invariance is by construction; its class (the maps preserving each sample’s cosines to the anchors, which include every orthogonal map times a positive scalar and every per-sample positive rescaling, but not translations) is the reader’s statement, re-derived in a dated note. The approximate agreement is the paper’s evidence: relative vectors match at cosine 0.86–0.97 across encoders, while ten-nearest-neighbour overlap is 0.10–0.39. It does not say the maps between trained spaces are isometries, which the source never measures (QUESTION-211), nor that the transfer needs no paired data: the anchors are paired data. | Active |
| THEORY-176 v2 | A task-loss stitching penalty compares representations in one decision problem, through a fixed top network and a restricted map class, so it is not Blackwell’s order: representations that are functions of each other can stitch differently, and a negative penalty shows the fitted map did not reproduce the layers it replaced | Bansal, Nakkiran & Barak (2021), LIT-850, define the stitching penalty L_ℓ(r; A) − L(A), with L_ℓ(r; A) the least task loss of A’s top layers fed r through a map from a simple family S, and use it to call one representation better than another. Read against Blackwell (1953), LIT-781, and THEORY-156, that ordering is one coordinate of the comparison of experiments with the decision rules cut down to A’s head composed with S. It is not invariant under Blackwell equivalence, which the paper intends, and it meets Blackwell’s order only where the fitted map reproduces the replaced layers exactly. The relations are this record’s derivations from the paper’s definitions, not the paper’s. | Active |
| THEORY-177 v2 | In a binary cyclic system, the Contextuality-by-Default measure of signalling is twice the sum, over contents, of the least direct influence of context that a canonical causal model of the data must place on each content, and each content’s least influence is the total-variation distance between its two marginals | Wang, Sadrzadeh, Abramsky & Cervantes (2021), LIT-851, Proposition 1. It joins CbD’s maximal couplings (LIT-777, Theorem 3.3) to Jones’s 2019 correspondence between couplings and canonical models, which the paper quotes and the record derives independently. The result measures signalling. Its minima are per content, each reached in its own model; one model reaches them all only if the system is noncontextual. It says nothing about contextuality beyond the bound that a rank-2 system with Δ ≥ 2 cannot be contextual, and identifies no particular causal model. | Active |
| THEORY-178 v3 | In an ensemble of sign-consistent Boolean rules on the 87-gene core of E. coli’s regulatory network, a transient knockout or overexpression of one gene can leave the network in a different attractor after release, and every gene that does so reaches a strongly connected component containing a positive circuit | Zhao, Wytock, Reynolds and Motter (2024), LIT-854. In an ensemble of sign-consistent Boolean rules on the 87-gene core of the E. coli regulatory network, 51 genes admit a transient knockout or overexpression that moves the network to a different attractor, and every such gene reaches a strongly connected component with a positive circuit. So one genotype may hold several heritable expression states without epigenetic marks, in the model. The evidence is a model ensemble, read in full in NOTE-655, and the title claims no more. No transient perturbation has been shown to have a lasting effect in cells; that experiment is QUESTION-172. | Active |
| THEORY-179 v2 | In Bhattacharyya et al.’s single-cell swarm assays of E. coli MG1655, the daughters of one mother swarmed alike at the fourth generation sampled and varied again at the seventh; swarm size correlated with a plasmid fepA-promoter reporter of Fur derepression by low iron (Spearman r = 0.71), and an iron chelator or added iron shifted swarming and held the shared state longer; a three-class switching model fitted to two time points matched the lineages only with a delay of three to four generations before switching, which the authors read as ruling out a bistable switch | Bhattacharyya et al. (2023), LIT-853. Single-cell swarm assays show sibling homogeneity in swarming at four generations and its loss by seven, a correlation (Spearman r = 0.71) between a Fur-repressed reporter and swarming, and longer persistence when iron is clamped. The iron link is read through a promoter reporter and is correlational, the inheritance rests on few founders and three time points, and the paper’s “memory”, “conditioning” and “decision-making” are functional labels, not evidence of learning. | Active |
| THEORY-180 v2 | In a tied single-head attention layer trained by ridge-penalized empirical risk minimization on high-dimensional Gaussian sequences, weight decay is a nuclear-norm penalty on the query–key map, and the learned map is a soft-thresholded noisy copy of the target: its outliers are recovered target directions and its bulk is finite-sample noise | Boncoraglio, Erba, Troiani, Xu, Krzakala & Zdeborová (2025), LIT-857: with S = WWᵀ, λ‖W‖²_F is exactly λ‖S‖_* (Appendix A), and in the limit n/d², p/d fixed the trained WᵀW/√(pd) has the law η·ReLU(S0 + δZ − εI), Z ∼ GOE, with δ a noise level that falls with the data and ε a threshold set by λ (Claim 4.1, replica/AMP, checked against Adam at d ≤ 400). It does not say that real transformers’ spectra arise this way: the data are isotropic Gaussian, the target is inside the model class, and the agreement with measured spectra is qualitative. | Proposed |
| THEORY-181 v3 | In a model that decodes the sum of two learned embeddings, at zero training loss with an injective decoder, a training set fixes the generalising representation of addition when its same-answer pairs leave only translation and scale free; for non-modular addition with p = 10 and one-dimensional embeddings, generalisation sets in near the training fraction, about 0.4, at which that becomes likely | Liu et al. (2022), LIT-858, in a toy built for it: same-answer training pairs force equal embedding sums, equal sums carry answers to unseen pairs, and for addition with p = 10 the fraction at which the forced equations first pin the embedding to a + kb (about 0.4) matches the onset of generalisation and Power et al.’s critical fraction (LIT-341). It is shown for one size, 1D embeddings and an operation built into the architecture. It is not shown that larger networks generalise by this mechanism, and for S₃ the networks generalise beyond it. | Active |
| THEORY-182 v2 | A rank-limited contrastive word embedding trained from small initialisation learns the top eigenvectors of the co-occurrence matrix’s relative deviation from independence, one at a time in order of eigenvalue, not the best low-rank approximation of its unconstrained optimum | Karkada, Simon, Bahri and DeWeese (2025), LIT-855: for the quartic approximation of word2vec with tied weights and symmetric, constant-weight reweighting, the minimisers are proved and the stepwise order is derived, and the prediction matches trained word2vec far better than truncated PMI. It is shown for a proxy of word2vec, not for word2vec, and the dynamics are an approximate derivation. | Proposed |
| THEORY-183 v2 | When the co-occurrence of words on a latent continuum depends only on their separation, a spectral word embedding places them on the Fourier modes of that continuum, so the circles and rippled curves of months, years and places come from a symmetry of the corpus statistics | Karkada, Korchinski, Nava, Wyart and Bahri (2026), LIT-860: proved for an embedding whose Gram matrix equals the co-occurrence matrix (or its absolute value) at full rank, with the exponential kernel solved for both boundary conditions; the symmetry measured in Wikipedia; matching PCA pictures in Gemma 2. That trained networks get their geometry this way is inferred, not tested: nothing in the paper changes the statistics and watches the geometry follow. | Proposed |
| THEORY-184 v2 | Under a permutation-equivariant update whose map is K-Lipschitz, coincident neurons stay coincident at every step size, and at step size below 1/K distinct neurons cannot merge in finitely many steps | Yang, Poggio, Chuang and Ziyin (2025), LIT-861, read in NOTE-663. If an update commutes with permuting neurons (GD, SGD or Adam on a permutation-symmetric loss) and its map is K-Lipschitz, one step of size η changes every pairwise neuron distance by a factor in [1 − ηK, 1 + ηK]. This is a proved constraint on trajectories. It does not say that training simplifies above 1/K, that neurons never merge in the limit, or that any scale-dependent shape of the neuron cloud is preserved. | Active |
| THEORY-185 v4 | When each binary attribute of a word affects its co-occurrence independently and multiplicatively, the PMI is affine in the attributes with rank at most d + 1, so a spectral PMI embedding is a linear image of the attribute hypercube and parallelogram analogies hold exactly; over the full hypercube of words, each attribute’s two values equally frequent, the raw co-occurrence ratio mixes in products of attributes, and keeps exact analogies only when the strengths are alike enough that every attribute mode outranks every product mode | Korchinski, Karkada, Bahri and Wyart (2025), LIT-863: proved for a generative model of co-occurrence in which words are bundles of independent binary attributes, with robustness to noise, pruning and deleted pairs argued from eigenvalue bounds and simulated. The embeddings are eigendecompositions, not trained models; that real co-occurrence is close to this form is inferred from spectral and accuracy-curve shapes, not measured. | Active |
| THEORY-186 v4 | A deep linear network trained from small weights learns the singular modes of its input–output correlations one at a time in order of strength, each in a sharp sigmoidal transition, while a shallow network learns them all together; the stages come from the product of layers and the data’s spectrum, not from nonlinearity | Saxe, McClelland and Ganguli (2019), LIT-862, restating their 2014 solution (LIT-864): exact for decoupled, balanced initial weights and white inputs, simulated for random small weights. With hierarchically generated data the spectrum falls with depth in the tree, so the schedule is coarse to fine. It is not a claim about nonlinear networks, about correlated inputs, or about learning that starts from prior knowledge. | Proposed |
| THEORY-187 v3 | In a deep linear network trained by gradient descent on whitened inputs from decoupled, balanced initial weights, depth slows learning through the initial end-to-end strength of each mode: counting iterations as learning time over the stable step size, from strength of order one the number of iterations stays bounded as depth grows, once the step size falls with depth as stability requires, while from small strength ε the plateau lengthens from ln(1/ε) with one hidden layer towards 1/ε at great depth | Saxe, McClelland and Ganguli (2014), LIT-864, Eqs. 13–17 and Appendix B: exact for decoupled initial weights and whitened inputs, with the step size bounded by the Hessian at the optimum, and supported on MNIST from decoupled starts up to 100 layers. It does not show that random orthogonal initialisation is such a start. The paper’s account of that, isometry of the product of layers, is argued and simulated, not derived. It says nothing about nonlinear networks’ learning time, and it is not advice on how to initialise. | Active |
| THEORY-188 v2 | In a random graph whose nodes lie in a hyperbolic disk and connect by distance, a power-law degree distribution and strong clustering follow from the geometry: the degree exponent is set by node density relative to curvature, clustering by a temperature, and removing the angular, metric part of the distance leaves the configuration model | Krioukov, Papadopoulos, Kitsak, Vahdat and Boguñá (2010), LIT-865: derived, in a large-distance approximation, for a model in the hyperbolic plane, with simulations. γ = 2α/ζ + 1; clustering falls from its maximum at T = 0 to zero at a transition at T = 1; a circle model with power-law hidden degrees is the same ensemble once degree is radial depth; dropping the angular term gives the configuration model. It does not show that any real network is hyperbolic, or that hierarchy causes heterogeneity. | Proposed |
| THEORY-189 v2 | Nested angular cones in the Poincaré ball, symmetric about the outward ray with an aperture depending only on the apex’s radius, are transitive only if the aperture is at most π/2 and r sin ψ(r)/(1 − r²) does not increase outward; so no such cone can be defined near the origin, the widest admissible family is sin ψ = K(1 − r²)/r, and every point a cone contains lies farther from the origin than its apex | Ganea, Bécigneul and Hofmann (2018), LIT-866: Lemma 2 and Theorem 3 prove the necessity half under four stated requirements on the cones; the transitivity of the closed-form family (Theorem 4), which the source asserts without proof, is proved in this record’s note of 2026-10-19; the radial monotonicity is this record’s derivation from the hyperbolic law of cosines. It says what a cone order on the ball can be, not which posets embed in it, and nothing about meets, joins or learned embeddings. | Active |
| THEORY-190 v3 | Under geometric coarse-graining of the S¹ hidden-metric network model, which merges blocks of r angular neighbours into supernodes linked if any of their members were, the supernodes’ link probability approaches the S¹ form with β kept, κ′ = (Σκ^β)^{1/β}, μ′ = μ/r and R′ = R/r, its ratio to that form tending to 1 as their separation grows large against the block width and the coupling μκ′κ″; between nearby supernodes it exceeds that form | García-Pérez, Boguñá and Serrano (2017), LIT-869: derived to first order, checked on one synthetic network over eight layers and on six real ones. Supernode hidden degree is the ℓ^β sum of its members’; β is invariant. The record proves the closure at large separation, with relative error of order β times the block width over the separation, and computes that between neighbouring supernodes the union of member links exceeds the S¹ form (by 32–86% in a worked example with two-node blocks). The source’s flow ⟨k⟩′ = r^ν⟨k⟩, with ν = 2/(γ−1) − 1 or 2/β − 1, rests on the closure at every separation and is QUESTION-203. It does not show that real networks are generated by a hidden metric space, or that the nested layers are a hierarchy found in the data. | Active |
| THEORY-191 v2 | In four natural odour sources (strawberry, tomato, blueberry and mouse-urine volatiles), the rank order of correlations between compound concentrations has the Betti-curve signature of points near the boundary of a three-dimensional hyperbolic ball, not of any uniform Euclidean cube tried, and human odour-descriptor profiles for 127 odorants have that of a full three-dimensional hyperbolic ball | Zhou, Smith & Sharpee (2018), LIT-872: for strawberry, tomato, blueberry and mouse-urine volatiles, and for Dravnieks’ perceptual ratings of 127 odorants, clique-topology Betti curves match a 3D hyperbolic model and reject uniform Euclidean cubes of every dimension tried. It does not show a tree in the data, and because the fitted odour model is a thin shell, it does not separate a hyperbolic metric from a sphere in flat space. | Active |
| THEORY-192 v2 | In twelve sessions of rat dorsal CA1 from three data sets, pairwise correlations among place cells have the Betti-curve signature of points sampled uniformly from a three-dimensional hyperbolic ball, not of a low-dimensional Euclidean cube, and the fitted radius rose with the logarithm of exploration time | Zhang, Rich, Lee & Sharpee (2022), LIT-876: in twelve sessions from three data sets, the rank order of CA1 spike correlations matched uniform samples from a 3D hyperbolic ball and not uniform samples from low-dimensional Euclidean cubes or shuffled data, and the ball’s radius rose with log exploration time from seconds to days. It does not show that the metric, as opposed to the distribution of field scales, is hyperbolic, nor that a tree is represented. | Active |
| THEORY-193 v2 | A simplicial complex grown by gluing each new d-simplex to one (d − 1)-face, by a rule that uses no geometry, has a 1-skeleton whose geodesic triangles are 2-thin at every size, so hyperbolic network geometry in Gromov’s sense is an outcome of the combinatorial growth; the equal-link drawing as ideal simplices is a convention, a tiling of the hyperbolic plane for d = 2 in the manifold flavor but not a tiling of hyperbolic d-space for d ≥ 3 | Bianconi and Rahmede (2017), LIT-867, read in NOTE-678, for the model, the degree law and the ideal-simplex drawing. The coarse hyperbolicity of the graph is the record’s: the source asserts the hyperbolic geometry through its drawing and measures nothing on the graph. Every such complex has a 1-skeleton with 2-thin geodesic triangles, whatever the flavor, so its hyperbolicity is a property of the network. The constant-curvature picture, ideal simplices in the Poincaré ball, is a choice of drawing. It tiles H² for d = 2 in the manifold flavor, and for d ≥ 3 it is not a tiling. This says nothing about whether real networks grow this way. | Active |
| THEORY-194 v5 | On Monte Carlo samples of the 2D Ising model and of the 2D dimer model with added noise spins, a block coarse-graining trained to maximize mutual information with the system beyond a buffer recovered the variables renormalization already uses (Kadanoff block spins; the dimers’ low-momentum electric fields, with no weight on the noise), and iterated on 128 × 128 Ising samples gave the flow away from the critical point, locating it to about 1% and giving ν ≈ 1.0 ± 0.15, while a restricted Boltzmann machine trained by contrastive divergence on the noisy dimer data coupled to the noise and to columnar patterns instead | Koch-Janusz and Ringel (2017), LIT-873: shown numerically on two 2D lattice models whose relevant variables were known (Ising block spins, dimer electric fields), with an iterated Ising flow giving T_c to about 1% and ν ≈ 1.0 ± 0.15, and analytically only for 1D and quasi-1D chains. The general equivalence of the objective with a short-ranged effective Hamiltonian is argued, not proved, and no system with unknown relevant variables was tried. | Active |
| THEORY-195 v3 | On the Random Hierarchy Model, in the experiments reported (s = 2, L ≤ 4, small v), deep CNNs matched to the tree and trained in a feature-learning regime reach a tenth of chance error from about n_c m^L examples, polynomial in the input dimension, at the training-set size at which their hidden layers become invariant to swapping synonymous tuples; two-layer networks and the same CNNs as fixed kernels need a number proportional to the whole input space, exponential in the input dimension, and deep CNNs stay near chance when every tuple is made equally likely in every class | Cagnetta, Petrini, Tomasini, Favero and Wyart (2023), LIT-877: measured for depth-(L + 1) CNNs and deep fully connected networks on the Random Hierarchy Model with s = 2 and L ≤ 4, with a large-v scaling argument for the correlation threshold and an exact one-step-gradient model of a two-layer network on one patch. The law n_c m^L is fitted, not proved for trained deep networks, and in this model the correlation threshold and the grammar’s size are the same expression, so the data cannot say which of the two sets it. | Active |
| THEORY-196 v2 | A finite tree embeds in the hyperbolic plane with worst-case distortion 1 + ε, but because a hyperbolic distance d takes about d bits to write, its coordinates need Θ((ℓ/ε) log deg_max) bits: logarithmic in the branching, linear in the longest path ℓ, so hyperbolic space is economical for shallow bushy hierarchies and not for deep ones | Sala, De Sa, Gu and Ré (2018), LIT-874. The upper bound is Sarkar’s construction with the paper’s bit count. The lower bound is proved for H² and one family of trees, with an approximation, and dimension’s help is shown only as an upper bound. The cost is a cost of coordinates in a fixed-point model, not of the information in the tree, and it says nothing about Euclidean or linear-direction representations of the same hierarchy. | Proposed |
| THEORY-197 v4 | Mehta and Schwab’s correspondence between Kadanoff’s variational renormalization group and restricted Boltzmann machines is an identity of parametrizations, under which an exact RG step is a perfect fit of the data distribution; away from that point it does not make training by distribution fitting a renormalization | Mehta and Schwab (2014), LIT-882, Eqs. 18–22: setting the RG kernel T = −E + H makes the RG coarse Hamiltonian equal the RBM’s hidden-marginal Hamiltonian for every parameter value, and Kadanoff’s exactness condition equal to zero KL divergence. Short of exactness the paper itself says the two use different variational schemes, and Koch-Janusz and Ringel (LIT-873) give a case where distribution fitting keeps the wrong variables. The free-energy part of the argument was derived independently here; Lin, Tegmark and Rolnick’s v2 appendix makes it in substance (LIT-887). | Active |
| THEORY-198 v2 | For a finite-range lattice Hamiltonian, a block coarse-graining that keeps all the mutual information the block shares with the system beyond a buffer makes the coarse measure factorize across the block, in 1D and, in D dimensions, when capture by a hyperplane of blocks amounts to capture by each block; barring exact cancellation of existing couplings, the renormalized Hamiltonian then gains no range, and in 1D product disorder gains no correlations across the block. The coarse-grainings actually optimized fall short of that condition, and for them the link is computed only for two-spin blocks of 1D Ising chains | Lenggenhager, Gökmen, Ringel, Huber and Koch-Janusz (2018), LIT-881: proved in 1D, and in D dimensions under an extra per-block assumption and barring fine-tuned cancellations. The full-capture condition is not met in the paper’s own worked case (decimation of two-spin Ising blocks keeps about half the information), and the decay of longer-range, many-spin and disorder-correlation terms as more information is kept is shown perturbatively for two-spin blocks of 1D chains only, and is monotonic only locally. | Active |
| THEORY-199 | In data generated by a random hierarchical grammar, the Bayes-optimal denoiser recovers the top-level class only below a threshold noise, which becomes sharp as the tree deepens and exists only when the grammar uses a small enough fraction of possible tuples (branching times that fraction below one), while low-level features degrade smoothly with noise and so survive past the threshold | Sclocchi, Favero and Wyart (2024), LIT-884: an annealed mean-field map of belief propagation on the Random Hierarchy Model, with its fixed points, checked against exact BP on single rule draws at s = 2, v = 32, L = 10. Not proved for quenched rules, a statement about an ideal denoiser that knows the grammar, not about a trained diffusion model. | Proposed |
| THEORY-200 v2 | On sparse hierarchical data, deep networks become insensitive to swapping synonymous parts and to small displacements of informative features at the training-set size at which they learn the task | Tomasini and Wyart (2024), LIT-880: measured for locally connected, convolutional and fully connected networks on the Sparse Random Hierarchy Model with s ≤ 3 and L ≤ 3, with thresholds for the two sensitivities tuned per setting; the sample size is about (s0 + 1)^L n_c m^L times s^(L/2) without weight sharing, with a one-step argument for the (s0 + 1)^L, and about (s0 + 1)^2 n_c m^L with it, unexplained. Both invariances keep the parent’s label statistics by construction, so the model shows that trained networks do the grouping, not that the invariances could not separate, and the extension to images is an analogy. | Proposed |
| THEORY-201 v2 | In next-token prediction on hierarchically generated sequences, the correlation between two tokens falls by about a factor m per level of their common ancestor, so a training set of P sequences resolves correlations only out to a distance t*(P) at which they meet sampling noise; learners come to represent the hidden symbols up to that depth, giving loss steps at about v m^(2ℓ−1) examples, and on character-level text the context at which the loss saturates grows as P^(1/(2β)) with β the measured correlation decay | Cagnetta and Wyart (2024), LIT-883, extending LIT-877 from labels to masked tokens: the correlation plateaus and the noise floor are derived for the Random Hierarchy Model in the large-v, large-m limit; the loss steps and the representation probes are measured in small transformers and CNNs; the link between them is argued, not proved; and the real-text evidence, from two character-level corpora, tests the effective context window, not the hierarchy. | Proposed |
| THEORY-202 v3 | In variational renormalization over general Boltzmann machines, neither a matched partition function nor Kadanoff’s exact trace condition makes a coarse-graining a renormalization: the first holds for joint Hamiltonians whose marginal is not the data, the second for hidden variables that do not interact with the system, so the variables a renormalization keeps must be fixed by a further stated condition | Lin and Tegmark (2016), LIT-887, arXiv v1–v2 appendix, a part dropped from the journal text: a family of joint Hamiltonians with Z_tot = Z and the wrong marginal, and the remark that any non-interacting pair meets the trace condition. Under Mehta and Schwab’s identification (LIT-882) the trace condition is a perfect fit of the data, so even an exact variational RG step leaves the coarse variables’ meaning free. The restricted Boltzmann machine proper needs visible–visible terms for the second construction; that narrows the example, not the claim. Promoted on 2026-10-20 with both constructions re-derived. Whether the trace condition suffices inside Kadanoff’s kernel families is QUESTION-205. | Active |
| THEORY-203 | In data generated by a random hierarchical grammar, the tokens that Bayes-optimal noising and denoising changes do so in blocks set by the depth of the latent that changed, and the block size, measured as the correlation length of the changes, diverges at the noise threshold where the top-level class is lost, as a power of the distance to it whose exponent is log(branching) over log(slope of the level-to-level belief map at its unstable fixed point); a Gaussian field with power-law spectrum has instead a correlation length of changes that grows with noise to the end of the process | Sclocchi, Favero, Levi and Wyart (2024; ICLR 2025), LIT-886: an annealed mean-field computation of the pair statistics of token changes in the Random Hierarchy Model, a scaling argument for the exponent, and one data collapse against exact BP at v = 32, m = 8, s = 2. It builds on the threshold of THEORY-199 and inherits its limits. Not about trained diffusion models, and not evidence that text or images are hierarchical. | Proposed |
| THEORY-204 v3 | On TinyStories and WikiText-103, the data-limited exponent of transformer test loss, fitted to the lower envelope of learning curves across context lengths at up to about 10^8 training tokens, overlaps γ/(2β), where β is the decay with lag of the top singular value of the token–token covariance and γ the decay of next-token conditional entropy with context length; under assumed per-lag scaling forms, a horizon n*(P) ~ P^(1/(2β)) gives the exponent min(δ, γ/(2β)), δ being the decay rate of the within-horizon excess losses | Cagnetta, Raventós, Ganguli and Wyart (2026), LIT-888, building on LIT-883’s effective context window. Under assumed scaling forms for the conditional entropy and for each lag’s learning curve, the exponent is min(δ, γ/(2β)) (re-derived 2026-10-20). Measured on TinyStories and WikiText-103, with transformers up to about 10^8 tokens and horizons of tens of tokens, the fitted exponent overlaps γ/(2β), best near the start of the envelope; γ is estimated from trained models’ own n-gram losses. Whether the horizon is why is open (QUESTION-233). | Active |
| THEORY-205 v2 | For a short-range lattice model on a cylinder with a symmetric transfer matrix whose leading excited eigenvalue is non-degenerate, with block and environment as slabs L_B transfer steps apart, the uninformative information-bottleneck encoder first loses stability at β = (λ0/λ1)^(2L_B), in the direction of the boundary weak value of the leading excited eigenvector, which by the cited conformal finite-size relation is the lowest-dimension primary at large circumference; the uninformative encoder can stop being optimal at a smaller β, and nothing is shown for blocks inside a buffer shell or for the fixed-alphabet RSMI optimum | Gordon, Banerjee, Koch-Janusz and Ringel (2020), LIT-885, Eqs. 3–5 and B2–C11, with one numerical check on a three-site critical Ising cylinder, reproduced exactly in NOTE-690. The theorem holds for slabs of a cylinder, at the point where the uninformative encoder first loses stability. The global first transition can come earlier, and when the two coincide is QUESTION-185. The paper’s “equivalence” of IB and RG relevance, and LIT-878’s use of it for RSMI filters on planar blocks, go beyond it. | Active |
| THEORY-206 v2 | For networks of smooth units without biases, one hidden layer needs exactly ∏(rᵢ+1) neurons to match the monomial x₁^r₁⋯xₙ^rₙ’s Taylor polynomial at the origin, and a deep network O(Σ log rᵢ), with the upper bounds holding for uniform approximation too, so the cost of flattening a polynomial grows exponentially with its degree in distinct variables and not with the number of inputs: products of many inputs separate depths, bounded-degree polynomials do not | Rolnick and Tegmark (2017), LIT-890, Theorems 4.1 to 4.3, extending Lin, Tegmark and Rolnick’s 2ⁿ for a product (LIT-887). Proved for Taylor matching at the origin with bias-free units; the uniform version’s lower bound rests on an unproved step. The flip side, that a polynomial of degree d with c monomials costs one layer at most c·2ᵈ however many inputs it has, is the edge: the separation does not reach the low-order polynomials LIT-887 calls natural. | Active |
| THEORY-207 v2 | Responsibility for a morally loaded outcome that emerges from morally neutral interactions in a network of agents can be allocated without fault or intention, by default and overridably, in full to every causally accountable node, and a rule so allocating it, made common knowledge, works as a corrective that prevents such outcomes | Floridi (2016), LIT-899, read in NOTE-699. A distributed moral action is an outcome no one intended. Floridi proposes holding every causally accountable node “prima facie equally and maximally responsible”, overridably, with the rule publicly announced so that agents restrain one another. Proposed: the rule is a design argued by analogy and by two court cases. In one of those cases the default is overridden by ease of rectification, which is a control criterion. It does not show that what is allocated is moral responsibility rather than accountability used as a corrective signal. | Proposed |
| THEORY-208 | Agency is multiply realisable without cognition or mental states, and AI is a new kind of it | Floridi (2025), LIT-897, read in NOTE-702, with the criteria taken from Floridi & Sanders (2004), LIT-898. In the record’s reading, agency comes in kinds. All of them share interactivity, and the richer ones add graded autonomy and adaptability. The kinds are told apart by origin, mechanism and where their goals come from, not by intelligence. AI is computational agency with data-driven learning, serving goals set by humans, with no intelligence or mental states. Proposed: the paper assumes that AI is an agent, does not argue for this thesis over its rival, asserts that AI lacks intelligence, and never states the level of abstraction its comparison uses. | Proposed |
| THEORY-209 v2 | A converged network trained with SGD is not at a point and does not sample its training loss: under a quadratic approximation it samples a Gibbs distribution on a modified loss, isotropic in the Hessian’s column space, with probability currents that keep it oscillating, so its speed and spread are set by the learning rate, momentum and batch size | Kunin et al. (2021), LIT-1011, read in NOTE-711. Modelled as an underdamped Langevin equation with noise covariance proportional to the Hessian, SGD at the end of training converges to a nonequilibrium stationary state: Gibbs on a modified loss whose curvature undoes the Hessian’s anisotropy, with inverse temperature S(1 − β²), in broken detailed balance. A ResNet-18 on ImageNet explores isotropically in a plane where the loss is anisotropic, oscillates at Hessian-dependent rates, and moves at the predicted speed across a hyperparameter sweep. For the learned-structure line, a trained solution is in part a property of the regime that trained it. Proposed: the deep-learning evidence is one network, under assumptions the paper concedes are strained. | Proposed |
| THEORY-210 v2 | Continuous parameter symmetries stretch a network’s minima into connected manifolds along which the loss is flat, and give gradient flow conserved quantities that fix where on such a manifold training ends; finite steps, gradient noise and weight decay break them, so the position along a symmetry orbit is set by initialization and optimizer, not by the loss | Zhao, Walters & Yu (2025), LIT-970, read in NOTE-712: a survey, so the dynamical results are secondhand. Continuous parameter-space symmetries (GL, scaling, orthogonal, translation) make minima positive-dimensional and connected, which is one source of mode connectivity. Under gradient flow each gives a conserved quantity, such as layer imbalance, that is fixed by initialization and locates the endpoint on the manifold. Under SGD these are not conserved. Read first-hand (Neural Mechanics; Ziyin et al.), weight decay drives the conserved quantities toward zero, and minibatch noise drives a rescaling symmetry’s toward the point where the layers’ gradient noise balances. The survey had reported this as imbalance decaying with large learning rates, and a stationary distribution biased toward balanced solutions that a Langevin model does not predict. This is the null-space half that THEORY-209’s limiting dynamics leave out. Proposed: one survey, with the SGD results unread here. | Proposed |
| THEORY-211 v3 | In the stochastic-differential-equation model of SGD, with a gradient-noise covariance that depends on the parameters, minibatch noise drives the difference of squared norms along a rescaling symmetry, at a rate proportional to learning rate over batch size, to the point on the symmetry orbit where the gradient-noise traces of the two parameter groups are equal, whenever both groups carry noise; so at stationarity SGD neither keeps the difference fixed, as gradient flow does, nor lets it diffuse, as isotropic noise does, and differs from gradient descent by a finite amount however small the noise | Ziyin, Li & Ueda (LIT-1012, read in NOTE-714), with the gradient flow conservation law and the Itô term from Neural Mechanics (LIT-1013). If ℓ(u, w) = ℓ(λu, w/λ) for every sample, then under the SDE model of SGD d(‖u‖² − ‖w‖²)/dt = −T(uᵀC₁u − wᵀC₂w), with T = η/S. The noise has no component along the symmetry, but its dependence on the parameters produces a deterministic drift through Itô’s lemma. The drift points to the noise-balanced point, and weight decay adds to its rate. In a diagonal linear network the stationary distribution follows exactly: it is non-ergodic, has a memory of initialization, and collapses to zero above a critical temperature. The law is re-derived here (2026-10-19) within the SDE model; the tests are small synthetic networks, and whether it holds in deep networks on real data is QUESTION-164. | Active |
| THEORY-212 | In a two-layer linear network trained by gradient flow, the relative scale of the two layers, which gradient flow conserves, sets the learning regime: balanced layers learn in sigmoidal stages and both build task-specific representations, while strongly unbalanced layers learn exponentially with a static kernel and leave the larger layer task-agnostic | Dominé et al. (2025), LIT-943, read in NOTE-715. With whitened inputs and a λ-balanced start, W₂ᵀW₂ − W₁W₁ᵀ = λI, the full gradient flow is solved exactly. λ is conserved and sets the regime. As λ → 0, singular values are learned in sigmoidal stages, as in Saxe et al., and both layers become task-specific. As |λ| → ∞, learning is exponential, the NTK is static, and the larger layer stays near the identity while the smaller carries the task at scale ∝ 1/|λ|. The paper analyses gradient flow only. Under SGD the conserved quantity drifts (THEORY-211), which QUESTION-081 takes up. | Proposed |
| THEORY-213 v3 | Every mirror symmetry of a network’s per-sample loss makes its symmetric subspace invariant under gradient descent and SGD, and when the loss’s Hessian is bounded below by −c, weight decay γ‖θ‖² with γ > c/2 puts every minimum in that subspace; rescaling symmetries that hold at λ = −1, rotation symmetries and permutation symmetries contain such mirrors, whose subspaces are zeroed weights, reduced rank and identical neurons | Ziyin (2024), LIT-1014, read in NOTE-716. If a per-sample loss is invariant under the reflection I − 2OOᵀ, then Oᵀθ = 0 is a stationary condition for GD and SGD. The Hessian is block diagonal there. Above a critical weight decay all minima satisfy the constraint. Under SGD with strong noise the subspace is attractive even at a strict saddle, by a Lyapunov-exponent argument. Rescaling, rotation and permutation symmetries imply mirrors, so they yield sparsity, low rank and merged neurons, with collapse and loss of plasticity as consequences. The SGD half is approximate and the network evidence is limited; the title holds only the exact half. Promoted on 2026-10-20 on the exact half, re-derived. The SGD half is QUESTION-206. | Active |
| THEORY-214 v2 | On the 2022 r/place canvas, the abrupt overthrow of a crowd-built image from a stable period is predicted up to hours ahead, on held-out images and on the 2023 edition, by a combination of many image-level series far better than by any generic slowing-down indicator; the series the predictor relies on include low past restoring of attacked pixels as well as attack outrunning restoration, and about a quarter of overthrows give no warning at the 20-minute range | Falmagne, Stephenson & Levin (2026), LIT-1025, read in NOTE-731. On about 10,900 compositions of 2022, a predictor of time-to-overthrow built from 19 composition-level series with a 7-hour memory catches half the overthrows within 20 minutes at 3.6% false positives, beats variance and autocorrelation trends, and transfers to 2023. Its precursors are many: attack outrunning defence, a turbulent history, little accepted change, uncoordinated activity, simple images, low past defence; slowing down and speeding up both occur. About a quarter of overthrows are unpredictable at the 20-minute range. The social readings of the precursors are the authors’ conjecture from SHAP curves; nothing here measures plans. | Active |
| THEORY-215 | A Hawkes process with a Lipschitz rate function and signed kernels has a unique stationary regime, which suitably started versions approach, when the Lipschitz-weighted absolute kernel mass is below one (a spectral radius below one, for a network) or when the rate is bounded | Brémaud and Massoulié (1996), LIT-1035, read in NOTE-728: Theorems 1, 2, 7 and 8, proved. Inhibition is allowed because the conditions use |h|. The conditions are sufficient, not necessary; the kernels are fixed in time; uniqueness is among solutions with finite mean intensity. In the linear excitatory case the condition is the branching ratio below one, but in the nonlinear signed case the spectral-radius quantity is a bound, not a branching ratio, and a bounded rate needs no bound on the kernels at all. Nothing is proved about cascade sizes or about what happens past the threshold. | Active |
| THEORY-216 v3 | On the 2017 r/place log, with coalitions recovered from co-placement, which coalitions survive is barely predictable early from their size, area, start time and colour entropy, the size distribution of recovered coalitions shifts toward large ones as the event proceeds, and some lasting artworks were held by coalitions that kept working under sustained overwriting | Wu & Silva (2024; v3 2026), LIT-1032, read in NOTE-724. On the 2017 r/place log, coalitions are recovered, failed ones included, from co-placement and image segmentation. Under 7% of updates survive to the end. Recovered coalition sizes shift toward large over the event. A decision tree on four state features predicts survival at F1 0.09 in the first 48 hours and 0.67 later. Illustrated successful coalitions keep working under overwriting throughout, and some failures look like successes until a late collapse. The recovery is validated only against final artworks, the lifecycles are ten examples, and nothing here observes plans. | Active |
| THEORY-217 | A trait malfunctions when its operation does not correlate positively with the normative field, the minimum change its organization’s viability requires at each precarious state; malfunction needs no second order of regulatory norms, and regulatory traits can malfunction by the same standard | Barandiaran (2025), LIT-1026, read in NOTE-730. Against the dual-order account (Saborido, Moreno and Mossio), on which malfunction needs a regulated switch between regimes that a first-order trait fails to follow. The viability space has viable, precarious and terminal regions, and the normative field is the minimum constant parametric change at each precarious state that avoids disintegration. A trait functions when it correlates positively with the field, subfunctions when it does so too slowly, malfunctions when it does not, and is nonfunctional when it does nothing where it must. The standard is the organization’s own viability, not a designer’s goal, a selection history or a statistical norm. Proposed: a conceptual proposal with a one-variable model, and the field has not been computed for any real organism. | Proposed |
| THEORY-218 v2 | In one case study of the 2017 r/place Mona Lisa, what was added to or removed from the image was, once its forum opened, decided off the canvas, in a forum of 161 accounts negotiating through linked design images, where a few central members admitted or refused additions, and the forum’s changes then appeared in a region where about 77,000 accounts placed tiles, most of whom never posted; how many placers followed the designs is not measured, and the authors argue that the placement record alone cannot show who directed the image or who cooperated | Litherland & Mørch (2021), LIT-1037, read in NOTE-733. For the 2017 Mona Lisa, 76,774 accounts placed tiles in the region while a forum of 161 negotiated the design through linked blueprints. Central members admitted a Swiss flag and a rainbow frame and erased r/trees objects, and a tag on the image recruited newcomers. Whether an addition was vandalism or part of the image was settled by negotiation. The authors argue placement data cannot reveal cooperation, conflict or affiliation. One artwork; the link from forum power to placements is “unclear” by the authors’ account; their “instruction” is Reddit’s rules, not planners’ orders. | Active |
| THEORY-219 v2 | Agency in the sense that bears on responsibility needs a standpoint that settles and carries forward revised evaluative standards when its inherited ones break down, and planning, autonomy, memory and coordination do not supply one | Kahl (2026), LIT-1033, read in NOTE-723. “Continuity pressure” arises where an inherited evaluative frame no longer settles how to go on, and the revision must be carried forward by the same standpoint rather than imposed from outside, escaped by rollback, or chosen by a fixed higher-order rule. Representative agentic systems ordinarily fail it because their failures are corrected from outside. A necessary condition for attributive agency only, argued from cases and never measured; the line between settling a frame and selecting under an antecedent rule is not made precise. | Proposed |
| THEORY-220 v3 | A far-from-equilibrium system that contributes to its own maintenance has functions relative to itself, with no history or observer needed, and one that switches among self-maintaining processes has indications of success that can be false by its own lights | Bickhard (2000), LIT-1029, read in NOTE-729. Function is contribution to a far-from-equilibrium system’s own persistence; the asymmetry between persisting and decaying gives function and dysfunction, always relative to the system served, so a parasite’s gut serves the parasite and harms the host. A candle flame has functions in this sense. Representation arrives with recursive self-maintenance: a system that picks its next interaction by how it has differentiated its environment implicitly predicates that the interaction will succeed, and can find the predication false. Proposed: a conceptual account, with no model, whose account of having a function (and so of malfunction) is deferred to another paper. | Proposed |
| THEORY-221 v2 | Organizational closure is a circular organization of efficient causes by which a system produces the conditions of its own existence, distinct from feedback, self-organization and catalytic cycles; systems whose loops do not regenerate the constraints that make them possible approximate closure without instantiating it | Rubin, Roli, Stano & Damiano (2026), LIT-1027, read in NOTE-727. A genealogy of closure notions from logic, cybernetics, systems theory, thermodynamics, relational biology and the biology of cognition, and an interpretive thesis drawn from it. The genealogy shows that “closure” names different things (information, operations, efficient causes, constraints, catalysts). The thesis picks efficient causes, adds that closure so read cannot be exhaustively described as a state-determined syntactic procedure, and concludes that current AI, agentic LLM systems included, is heteronomous. Proposed: the thesis is an interpretation, the irreducibility rests on Rosen’s unassessed arguments and a halting-problem argument the authors call provisional, and the AI verdict is drawn from the definition, not from analysis of any system. | Proposed |
| THEORY-222 v5 | With uniform interventions imposed separately at each level, a coarse-grained macro description of a known discrete mechanism can have more effective information than the micro description it supervenes on, so the level at which effective information is highest can be a macro level | Hoel, Albantakis & Tononi (2013), LIT-1038, read in NOTE-726. Effective information is effectiveness (determinism minus degeneracy) times the log of the state-space size, measured under uniform interventions. Coarse-graining always loses size and can gain effectiveness; when the gain wins, causal emergence CE = EI(macro) − EI(micro) is positive. Four toy systems give 0.40 to 2.92 bits. The arithmetic is exact. The reading that the EI peak marks where causation happens rests on imposing a uniform distribution at each level, which the paper adopts and does not test; the title does not claim it. Promoted on 2026-10-20 on a construction. Whether the gain survives one intervention distribution at both levels is QUESTION-204. | Active |
| THEORY-223 | When the rules that govern a system lie within its own action space, the governor’s authority rests on the system leaving them alone, and further controls in the same space inherit that dependence | Lahiri (2026), LIT-1039, read in NOTE-732. In agent frameworks that keep configuration as files the agent can read and write, the coordination architecture sits inside the technical subsystem’s action space, and the social subsystem’s authority “depends on the agent’s continued acceptance of-or inability to circumvent-the constraints”. Permission lists and sandboxes kept in the same space inherit the exposure; only constraints outside it escape. Argued from one platform’s architecture. The paper’s vignettes show agents adding channels and artifacts, not altering a control, so the recursion itself is argued and not observed. | Proposed |
| THEORY-224 v2 | Objects on a crowd-built canvas are of two kinds, those that spread by a local recolouring rule and are predictable from the canvas itself, and those copied from designs coordinated off the canvas, which local canvas dynamics do not predict | Adams, Fernandez & Witkowski (2022), LIT-1034, read in NOTE-725. A CNN predicting each pixel of the 2017 r/place canvas from its 3×3 neighbourhood recovers objects that grow by recolouring neighbours (Blue Corner, German flags) and misses designs whose plan lived off the canvas (EU dove, US flag) at a six-hour horizon. Short-horizon predictability dips mid-event. The evidence is one illustrated output and SSIM curves with no persistence baseline. The paper models no participants and does not measure anyone’s reach. | Proposed |
| THEORY-225 | No single-mechanism analysis of ordinary manipulation fits the clear cases: covert influence, covert intent, non-rational influence, trickery and pressure each misclassify a familiar tactic, so what unifies manipulation is unsettled | Noggle, SEP (2018, rev. 2026), LIT-1007, §§2.1–2.4, read in full in NOTE-744. A survey that argues for little; this is its one conclusion with moderate support, reached by giving each family of analyses a familiar tactic it misclassifies. The cases rest on shared intuitions about clear instances, not on argument. It leaves open common-factor and non-definitional accounts, and it is about ordinary manipulation, not the global manipulation of the free-will literature. | Proposed |
| THEORY-226 | LLM revisions of an essay move it further in sentence-embedding space than its author’s own revision does, and in a direction shared across essays, models and prompts | Abdulhai et al. (2026), LIT-997, read in NOTE-750, §4.2 and Figs. 1, 5, 13–25. Three LLMs revising 86 ArgRewrite-v2 drafts under five prompts moved them further than the students’ own 2021 revisions did, and in one common direction, under two embeddings. Shown in plots, with no distance, angle or test. Meaning is measured only as embedding position: the paper does not show that the writer’s intended meaning changed, and the “grammar” prompt came with content feedback. | Proposed |
| THEORY-227 v2 | Mutual information between an input and its representation does not fix the representation’s quality: invertible encoders all preserve it exactly, yet under a linear probe some do better than the raw input and some worse | Tschannen, Djolonga, Rubenstein, Gelly & Lucic (2020), LIT-247, read in NOTE-749. Invertible RealNVP encoders on MNIST halves keep the true MI constant, yet trained with an MI estimator they gain linear-probe accuracy, and one trained adversarially against a linear probe ends “significantly worse than using raw pixels”. At matched bound values the encoder architecture decides quality. What makes MI-trained representations good must therefore come from somewhere other than MI. The paper’s alternative, that InfoNCE works as metric learning, is argued, not tested. | Active |
| THEORY-228 v2 | On a finite augmentation space, at the population optimum of the spectral contrastive loss with k ≥ 2r, linear-probe error is bounded, up to constant and logarithmic factors, by the error of recovering the label from an augmentation divided by the squared sparsest-partition conductance of the augmentation graph | HaoChen, Wei, Gaidon & Ma (2021), LIT-249, read in NOTE-740. On a finite augmentation space, with labels recoverable from augmentations up to error α and k ≥ 2r, every population minimizer of the spectral contrastive loss has linear-probe error Õ(α/ρ²_⌊k/2⌋), where ρ is the sparsest-partition conductance of the augmentation graph (Thm 3.8). The guarantee needs no conditional independence of the views given the label. It is a statement about the population optimum of one loss: it says nothing about what training reaches, nothing about InfoNCE, and its infinite-space extension is asserted, not proved. | Active |
| THEORY-229 v3 | For a symmetrized Barlow Twins loss on a linear or fixed-kernel model, gradient flow from a small initialization of common scale aligned with the top eigenvectors of the pairs’ symmetrized cross-correlation learns them one at a time, in order of eigenvalue, and ends at a top spectral solution, which is exactly a minimum-norm zero-loss solution: kernel PCA on K_Γ | Simon et al. (2023), LIT-242, read in NOTE-741. For L = ‖C − I‖²_F with λ = 1, no batch norm and C symmetrized by hand, a linear model from aligned initialization learns mode j at τ_j ≈ −log(s_j(0)²γ_j)/(8γ_j) (Prop. 4.1, proved), the top spectral solutions are exactly the minimum-norm zero-loss ones (Prop. 4.3), and the kernel version is kernel PCA on K_Γ (Prop. 5.1). Generic small initialization is covered by an informal derivation only. The operator is built from the model’s kernel and the sample pairs, not from the positive-pair density ratio, and the stepwise growth seen in ResNets under SimCLR and VICReg is an experiment, not a consequence. | Active |
| THEORY-230 v2 | The Fisher–Rao geometry of a language model’s next-token laws over a set of contexts is a function of those laws alone, so models with identical laws share it, while activation geometry changes under invertible reparameterizations of the hidden layer that leave outputs unchanged; in Picozzi’s ten transformer, state-space and recurrent models it agreed at a mean rank correlation of 0.88 against 0.62 for activation geometry, and about 9% of the top eigenvector overlap exceeded a null matched to the shared laws | Picozzi (2026), LIT-936, read in NOTE-755, a single-author v1 preprint with code on request. The matrix of Fisher–Rao distances between a model’s next-token laws on a context battery is invariant to every output-preserving reparameterization, while activation geometry has a GL(d) gauge (Prop. 1); two models with identical outputs can have hidden geometries that rank-correlate at −4/17 (Prop. 3). Over ten transformer, state-space and recurrent models the mean rank agreement is 0.88 against 0.62 for mid-layer activations. Convergence is proved only as a consequence of each model’s excess risk to a common law, and that bound is vacuous on real models. Against a law-matched null, about 9% of the top-six eigenvector overlap is shared beyond the laws. Promoted on 2026-10-20. Replication and a test that varies the law are QUESTION-216. | Active |
| THEORY-231 v3 | Within classical realism, a generalized-noncontextuality no-go refutes Leibnizian representations, not realist representations as such; it rests on a stronger assumption than a Bell-like no-go and so applies where none exists, as in prepare-measure scenarios, but only Leibnizianity implying noncontextuality is proved | Schmid, Selby and Spekkens (2020), LIT-945, §VI.C, §VIII (Eqs. 200, 214, 215), read in part in NOTE-737, which is Skimmed: §§II–IV and the proofs in Appendices C–G were not read. A Leibnizian classical realist representation implies a generalized-noncontextual one, so every noncontextuality no-go is a no-go for Leibnizian representations. The converse is Conjecture 1′, so a Leibnizianity failure is not shown to be a noncontextuality failure. The prepare-measure claim is stated, not derived, in the text read. | Active |
| THEORY-232 | A whole can be compared in agency with its parts, relative to a chosen decomposition and the parts’ goals: it is more agential when its organization lets the parts resolve more of their mutual constraints than they do at the equilibrium of their former organization, which shows as delayed gratification | Watson (2023), LIT-990, read in full in NOTE-747. A perspective essay’s definition, argued and illustrated, not proved: agency of a whole with respect to its parts is the reduction in the parts’ total frustration at equilibrium that its organization achieves over the old one, shown by directed uphill excursions to lower minima. It is comparative and sets no threshold for an additional agent, and it holds only relative to a stipulated decomposition and stipulated goals for the parts. That bottom-up learning produces such organization is reported from earlier models, not shown here. | Proposed |
| THEORY-233 v2 | CKA and normalized Bures similarity are the Euclidean and the Bures comparison of normalized kernels, and each bounds the other only within a factor set by the kernels’ ranks, so agreement in one does not carry to the other with a dimension-free constant | Harvey, Larsen & Williams (2023), LIT-250, §5 and App. A.3, read in NOTE-753. CKA = 1 − ½‖K_X/‖K_X‖_F − K_Y/‖K_Y‖_F‖²_F, while NBS = 1 − ½B²(K_X/Tr K_X, K_Y/Tr K_Y), with B the Bures distance. They induce the same topology, but CKA/√(r(K_X)r(K_Y)) ≤ NBS² ≤ min[r(K_X), r(K_Y)]·CKA, saturated at rank 1. NBS bounds CKA of the square-root kernels, with equality for commuting kernels. Linear kernels only, and the discrepancy is illustrated on Wishart samples, not trained networks. | Active |
| THEORY-234 v2 | Two softmax next-token predictors induce the same distribution exactly when their embeddings and unembeddings are related by an invertible linear map on the subspaces that enter the logits, with arbitrary distortion off them, so a linear relational property is shared by all such models or none when it lies in those subspaces, and can fail to be shared otherwise | Marconato et al. (2024), LIT-950, read in NOTE-746. For p(y|s) ∝ exp(f(s)ᵀg(y)) on a shared vocabulary, p_{f,g} = p_{f̃,g̃} iff the models are extended-linearly equivalent: invertible linear maps between the subspaces M and N that enter the logits, at any dimensions and without the diversity condition (Thm 5). The dimension of M is then a property of the distribution. Relational linearity, linear subspaces and linear probing hold in all equivalent models or none when Γ ⊆ N and Γ_q ⊆ M (Thm 14), and parallelism is shared only within N (Thm 15). Exact equality of distributions only, and no experiments. | Active |
| THEORY-235 | Covert influence that exploits a person’s decision-making vulnerabilities harms her autonomy in the process of deciding, by making her opaque to herself, even when it benefits her; so it carries a harm in every case without being wrong in every case | Susser, Roessler and Nissenbaum (2019), LIT-1002, pp. 4–5 and 9–11, read in full in NOTE-745. An argument in a short policy essay, not a defence against objections. It holds of influence that is covert and exploits a vulnerability, which the paper stipulates is what manipulation is; Noggle’s survey (LIT-1007) shows that covertness is not necessary for manipulation, so the claim is filed of covert influence, not of manipulation as such. The paper claims a harm in every case, not a wrong, and never examines its own intent requirement. | Proposed |
| THEORY-236 v2 | A representational similarity index that is invariant to every invertible linear map takes the same value on all representations whose rank equals the number of examples | Kornblith, Norouzi, Lee & Hinton (2019), LIT-254, Theorem 1, read in NOTE-743. If s(X, Z) = s(XA, Z) for every invertible A, and rank(X) = rank(Y) = n, then s(X, Z) = s(Y, Z): any two full-row-rank representations of the same n examples are related by an invertible linear map. So when width reaches the number of examples, an index with that invariance, such as CCA, says nothing. The theorem fixes no group; the paper’s case for orthogonal invariance plus isotropic scaling is an argument from training dynamics, not a consequence of it. | Active |
| THEORY-237 v3 | The critic-based variational lower bounds on mutual information, Donsker–Varadhan, NWJ, MINE’s and InfoNCE, are relaxations of one unnormalized Barber–Agakov bound, and, when the joint and the product of the marginals are mutually absolutely continuous, each attains its supremum over critics only at a critic equal to the log density ratio up to a term its normalization leaves free, where every bound but InfoNCE equals the mutual information | Poole, Ozair, van den Oord, Alemi & Tucker (2019), LIT-246, read in NOTE-739. Writing q(x|y) = p(x)e^f/Z(y) in Barber and Agakov’s bound gives I_UBA, tight at f = log p(y|x) + c(y). Jensen gives Donsker–Varadhan, a tangent bound on the log gives TUBA and NWJ (unique optimal critic 1 + log p(x|y)/p(x)), and NWJ applied to a K-sample problem with the batch mean as normalizer gives InfoNCE. MINE’s bias-corrected gradient is the exact gradient of TUBA. A Monte-Carlo DV estimate is neither an upper nor a lower bound. The InfoNCE optimum is cited, not derived, in the source (the record derives it, note of 2026-10-19), and the bias–variance comparisons are on toys. | Active |
| THEORY-238 v3 | The expected generalization error of an encoder–decoder learner is bounded by the encoder alone, through the KL divergence of its train-and-ghost latents to a prior symmetric under label-preserving permutations, for any decoder; and under lossy compression the bound can stay finite for deterministic continuous encoders, whose lossless bound is infinite | Sefidgaran, Zaidi & Krasnowski (2023), LIT-245, read in NOTE-742. Theorem 4: E[gen] ≤ inf 2√((2·MDL + K + 2)/n) + ε, where MDL is the expected KL of the joint law of the latents of the training set and an independent ghost set to any prior invariant under label-preserving permutations, and ε is the distortion allowed by lossy compression. It holds for any decoder. With a product prior it reduces to sample-wise mutual information. The bound is never evaluated, the prior may depend on unseen ghost data, and a 2√((K+2)/n) floor remains. It does not prove that I(X;U) cannot bound generalization. | Active |
| THEORY-239 v3 | For any joint law of an input and a context, symmetric or not, the top-d left singular functions of the conditional-expectation operator attain the minimum, over d-dimensional spans, of worst-case linear-probe approximation error over tasks of compatibility at least 1 − ε, namely (s₁² − (1 − ε)²)/(s₁² − s²_{d+1}) when s_{d+1} < 1 − ε ≤ s₁, though other spans can tie | Zhai (2025), LIT-975, read in NOTE-770: Lemma 1.4, Theorem 3.2 and Theorem 3.4 with App. B. The operator g ↦ E[g(A)|X] runs from L²(P_A) to L²(P_X) and is never assumed self-adjoint; its singular value decomposition comes from composing it with its adjoint. The guarantee is for linear probes and approximation error at the population level only. The thesis never works a non-reversible kernel on one space; the note of 2026-10-19 works a three-state one. It says nothing of what a trained network reaches. | Active |
| THEORY-240 | Loss of consciousness under propofol and in chronic disorders of consciousness goes with reduced pairwise integrated information between default-mode regions that rank as gateways of a synergy-defined workspace, not between its broadcasters | Luppi et al. (2024), LIT-949, read in NOTE-799. In resting-state fMRI, the regions where synergistic interactions outrank redundant ones split by rank into gateways (mainly default mode) and broadcasters (mainly fronto-parietal). Pairwise ΦR, the whole-minus-sum Φ plus redundancy, falls between default-mode gateways in propofol anaesthesia, in 22 DOC patients, and against post-anaesthetic recovery. The original Φ shows no common decrease. The finding is correlational, pairwise and content-free. The gateway/broadcaster split is imposed by the method; only where its two classes fall is measured. | Proposed |
| THEORY-241 | Fitting the same function in the same architecture does not fix the internal decomposition: SGD reproduces three Picbreeder images from random weights without the reuse and factoring of the evolved networks, and perturbing its weights breaks the regularities that perturbing the evolved networks’ weights preserves | Kumar, Clune, Lehman & Stanley (2025), LIT-944, read in NOTE-771. For the skull, butterfly and apple CPPNs, SGD in the layerized evolved architecture fits the image, the network’s whole function on the grid. It shows no reuse of the symmetric parts, and single-weight and random-direction sweeps distort the output, where the evolved networks’ sweeps vary it meaningfully. Qualitative, curated and three images. The paper’s account of why, the order of discovery in open-ended search, and its extension to large models are conjecture. | Proposed |
| THEORY-242 v3 | A spiral of silence can make a small, fixed minority opinion look far more widespread than it is without any member changing belief, and in the model that shows it the network’s direct distortion of what members see is small | Vilone and Polizzi (2024), LIT-939, read in full in NOTE-810. In agent-based models on scale-free networks with fixed private beliefs, a hard-core minority drives 55–60% of agents, nearly all of them in the majority, into silence, so that expressed and perceived opinion lean far toward the minority. The friendship-paradox distortion is small and of no fixed sign. This is simulation only. Beliefs never change, so nothing here shows a community coming to believe the minority view, and the majority is overturned only when the minority exceeds about 30%. | Active |
| THEORY-243 v3 | In the three-unit identity network x ↦ x(1, 0, 1) ↦ (0, 2, 1)·h, aligning the input with the third unit and aligning it with the direction (h₁ + h₂)/√2, two alignments related by an orthogonal change of basis, pass every interchange intervention on the input equally, so interchange interventions on that variable alone do not fix which internal direction mediates it | Wu et al. (2024), LIT-961, Appendix A, and Makelov et al. (2023), LIT-968, Appendix A.3 and §8, read in NOTE-809 and NOTE-782. Both rotate the same three-unit identity network. The input aligns with h₃ in one basis and with (h₁ + h₂)/√2 in the other, equally well under interchange interventions on the input (re-derived 2026-10-20). The reply says intervening on further variables separates them; that was not checked. Makelov et al. rest their verdict on component boundaries; the reply rests its on the interventions performed. Shown exactly for one constructed network only; whether trained networks have such ties is open (QUESTION-234). | Active |
| THEORY-244 v2 | For a computable source distribution f, Shannon entropy and mutual information are the expectations of their Kolmogorov counterparts only to within the complexity of f: 0 ≤ E K(x) − H(f) ≤ K(f) + O(1), and I(X;Y) − K(f) − O(1) ≤ E I(x:y) ≤ I(X;Y) + 2K(f) + O(1); Grünwald and Vitányi’s matching statement for the distortion-rate function rests on a step the record has not verified | Grünwald & Vitányi (2004), LIT-224, read in NOTE-776. For computable f: 0 ≤ E_f K(x) − H(f) ≤ K(f) + O(1) (Thm 2.10), and I(X;Y) − K(f) < E I(x:y) < I(X;Y) + 2K(f) to O(1) (Thm 3.6), both re-derived by the record from domination of f by the universal distribution and the coding theorem; the entropy gap is attained by a point mass. The expected structure function is stated to bracket D_m(R) and to equal D(R) per symbol in the limit (Thm 6.27), but its right-hand step is asserted, so that bridge is not part of this account’s claim (QUESTION-208). Sufficiency links only one way (Thm 5.13). None of this holds for a complex or unknown source, or for one string. | Active |
| THEORY-245 v3 | In a preregistered multimodal test with clearly seen images, prefrontal cortex carried a seen image’s category but not its identity, and a face’s orientation at most weakly, while posterior cortex carried category, face orientation and the identity of objects, letters and false fonts, though not of faces; no prefrontal site showed the preregistered onset-and-offset response, and one, found in an exploratory analysis, responded at offset earlier than predicted | Cogitate Consortium, Ferrante et al. (2025), LIT-973, read in NOTE-812. In iEEG and fMRI, with Bayesian support for the nulls, and against a positive control, prefrontal cortex held category but no identity or orientation, and none of 655 prefrontal electrodes showed the onset-and-offset response GNWT predicted. It does not show these dimensions were unaccessed, or that prefrontal cortex lacks them in other signals: high gamma and BOLD only, no single units, and every image was seen. | Active |
| THEORY-246 v2 | Among ResNet-50s trained on ImageNet with nine objectives and stopped early, seven of which beat softmax cross-entropy’s top-1 by up to 0.9 points, fixed penultimate features with more class separation transfer worse by linear probe to datasets whose classes are mostly not ImageNet’s (Spearman ρ = −0.93 across the nine; mean accuracy 75.9% for softmax to 48.3% for squared error), and within cosine softmax a higher temperature raises separation and lowers that accuracy; the objectives’ representations differ mainly in the last third of the network, and full fine-tuning brings mean transfer to within 1.3 points across them | Kornblith, Chen, Lee & Norouzi (2021), LIT-1044, read in NOTE-762. Across nine objectives for ResNet-50 on ImageNet, penultimate class separation R² runs from 0.349 (softmax) to 0.845 (squared error), Papyan’s Tr(Σ_W Σ_B†)/C from 21.2 to 0.33, and mean linear transfer to eight new-class datasets falls with R² (Spearman ρ = −0.93), from 75.9% to 48.3%. Cosine-softmax temperature raises R² from 0.24 to 0.77 and lowers transfer from 76.0% to 58.9%. CKA puts the differences in the last third of the network; fine-tuning erases them. The cost is for new classes: relearning the training classes, more separation helps. Networks early-stopped near 92% training accuracy; one dataset; correlational across losses. Promoted 2026-10-20 on this one study (ADR-047 v3), narrowed to what it measured. | Active |
| THEORY-247 v2 | For finite action-free labelled Markov chains, the discounted bisimulation metric, defined as the unique fixed point of Ferns et al.’s equation, is a bicausal optimal-transport distance, and it equals the value of a finite linear program over occupancy couplings | Calo, Jonsson, Neu, Schwartz & Segovia-Aguas (2024), LIT-962, read in NOTE-757. For finite action-free chains with real labels r and discount γ, the bisimulation metric’s fixed-point equation is the Bellman equation of transport over bicausal couplings with cost (1−γ)|r(x)−r(y)|, so the two coincide. The transport cost equals 1/(1−γ) times the minimum of a linear objective over occupancy couplings, under flow and coherence constraints (Lemma 1, Theorem 1). It says nothing of systems with actions. Its link to trace distance is one-way and second-hand. | Active |
| THEORY-248 v2 | The expected generalisation error of a learning algorithm is at most √(2σ²R/n) + ε, where R is the least information about the sample carried by any surrogate output whose expected generalisation error is within ε; I(S;W) is the lossless case, and for an L-Lipschitz loss R is at most the rate-distortion function of the output’s law at distortion ε/(2L), so the bound is finite wherever that function is, including where I(S;W) is infinite | Sefidgaran, Gohari, Richard & Şimşekli (COLT 2022), LIT-236, read in NOTE-780. Theorem 4: |E gen| ≤ √(2σ²·R_E(ε)/n) + ε, where R_E(ε) is the least I(S;Ŵ) over surrogates within ε in expected generalisation error. For a Lipschitz loss R_E is bounded by the rate-distortion function of P_W (Corollary 6). Theorem 10 is a tail version over a KL ball. The block-coding meaning is proved for finite alphabets only. No bound is evaluated for a learned model, and every bound depends on the unknown data distribution. | Active |
| THEORY-249 | Whether a system has agency can be settled only relative to a reference frame: each of four conditions of agency (a boundary, being the source of action, meaningful goal-directedness and adaptivity) needs a commitment outside the system before it can be decided | Abel et al. (2025), LIT-969, read in full in NOTE-793. A four-page position paper, argued and not proved: each condition is shown two-valued under two plausible choices by citing an earlier result (Jiang; Kenton et al., LIT-909; inverse-RL underdetermination; Zadeh). The premises are existential and the conclusion universal, so what is supported is that some attributions of agency depend on the frame. That the choices are arbitrary is asserted, and the paper itself floats predictive power as a way to choose. | Proposed |
| THEORY-250 | DALL-E 3 renders single familiar relations well but is not robustly compositional: human-judged agreement falls when subject and object of an asymmetric relation are reversed and when two relations are combined, and its failures on reversed prompts are mostly wrong or role-swapped relations, not missing objects | Fu et al. (2025), LIT-938, read in full in NOTE-813. Three human-rating experiments on one model: the reversal drop is significant (t(29) = 3.67), the compositional result is descriptive, and the error analysis covers only images below 0.2 agreement. The authors’ explanation by training-data likelihood rests on a Spearman r of 0.09 against a GPT-3 proxy. The finding is about one generator, and the “>5 objects” failure often quoted with it comes from the vision-language models, not from DALL-E 3. | Proposed |
| THEORY-251 | In few-shot classification by a base language model, failures from the choice of examples or from relabelled categories leave the class representations separable and fail at the vocabulary readout | Kirsanov et al. (2025), LIT-946, read in NOTE-789: at five demonstrations, accuracy across draws of examples runs from below 0.1 to about 0.6 while final-layer manifold capacity barely moves, and consistently swapped labels fail while capacity matches gold labels. The readout explanation is inferred from that dissociation, not measured; base Llama-3.1-8B and Gemma-2-2B, mostly synthetic data. | Proposed |
| THEORY-252 | On computational functionalism, an intervention that changes no neural activity and no actual causal interaction can change consciousness, because a clamp that stays idle on the actual input removes the transitions on every other input | Gidon, Aru and Larkum (2025), LIT-1000, read in full in NOTE-818: a voltage clamp replaying a recorded response injects no current on the matching stimulus yet fixes the network’s transitions on every other, so on the Turing–Putnam definition the computation degenerates while nothing that happens changes. It is a conditional about the view, not evidence about experience; the simulation shows only what an ideal clamp does, and the premise that removing unexercised branches changes experience is cited, not defended. | Proposed |
| THEORY-253 v4 | In Liu, Liu, Michaud, Gore and Tegmark’s Geometry model of independent skills with orthogonal task vectors, simulation shows skills progressing together under gradient descent, the weaker taking about 1/p of the time, and in sequence under sign descent, a weaker skill progressing fast only once a stronger is done and the ratio of their times approaching 2; on a rotated quadratic the sequence appears under sign descent only when the loss’s eigendirections are misaligned with the coordinates | Liu, Liu, Michaud, Gore and Tegmark (2025), LIT-951, read in NOTE-794. The Geometry model has loss Σ p_i L((θ − θ₀)·t_i) with orthogonal t_i. In it, SGD learns task 2 in time ∝ 1/p₂, while SignGD holds task 2 back until task 1 is done and then takes a constant extra delay (t₂/t₁ → 2). A rotated quadratic shows the split only when its eigendirections are misaligned with the coordinates (Fig. 12). The record reproduced both. The order is frequency order either way. The evidence is simulation and one fitted ODE; a derivation and a trained-network test are QUESTION-193. Sequential onset caused by dependency between skills is a separate experiment, not part of this account. | Active |
| THEORY-254 | Tangle-defined cohesion matches network communities only where community structure is strongly delineated, and tangles of one to three vertices recur beside the ones that do | Salter-Duke (2024), LIT-955, a PhD thesis read in full in NOTE-814. Edge-connectivity tangles, computed exactly at low order on eleven small real networks, give communities close to standard methods where structure is strong (yeast PPI) and none or almost none where it is weak (karate club, C. elegans, college football at the orders reached), and where tangles divide a network some hold only one to three vertices. The relation is read by eye from eight networks, and the vertex sets depend on the author’s assignment rule. | Proposed |
| THEORY-255 v3 | In Aerts’s subspace model of Hampton’s membership data, and in any lattice whose membership weight is order-preserving, whatever its negation, taking concept conjunction and disjunction as meet and join cannot produce overextension or underextension, so a model of the guppy-type deviations must take conjunction as some operation other than the meet or drop the monotone weight, while the Kolmogorov-type deviations can be had from the meet of a non-Boolean subspace lattice | Aerts (2009), LIT-934, Theorem 9 and §§2.2–3.3, read in full in NOTE-808. The impossibility is a proof, and it needs only that membership is monotone in the subspace. The fits that place the k-type deviations in a tilted subspace lattice and the ∆-type ones in an emergent sector are models with free parameters, not tests. Negation appears only as the orthocomplement used to derive the conjunction model from the disjunction model; no negated concept is measured. | Active |
| THEORY-256 v3 | When a sequence generator’s latent dynamics factor as a tensor product, its predictive state embeds losslessly and linearly in orthogonal per-factor subspaces of total dimension Σ(d_n − 1); 4-layer GPT-2-style transformers trained by next-token prediction on five Mess3 and Bloch Walk factors settle near that dimension, in per-factor subspaces that are linearly independent and approximately orthogonal in their leading components, and under the token noise tested reach it first even when noise makes it lossy | Shai et al. (2026), LIT-986, read in NOTE-758. The lossless embedding is an elementary theorem (Prop. 2.2, Thm 2.3, App. A). The rest is experiment on five synthetic factors: about 10 effective dimensions against 242 for the joint state, approximate orthogonality in the first two components, and under token noise a collapse to the factored form before expansion. It does not show that the preference is architectural rather than a feature of training, a question the paper leaves open, and it varies neither the objective nor the data domain. | Active |
| THEORY-257 v3 | Dynamical independence, zero information flow from the microscopic history into a coarse-graining given its own history, fixes emergent macroscopic variables by the dynamics rather than by a chosen query, but for linear VAR models of order above 1 generically none is exact, and the optima are many | Barnett and Seth (2023), LIT-979, read in NOTE-791: definition (2.6), transitivity (App. A), the causal-graph form (2.12), the state-space closed form (3.18) and the genericity count (3.25)–(3.26). The target is the coarse variable’s own future, so no outside query is chosen. But the system/environment boundary, the scale and the class of maps are inputs, and the worked theory’s candidates are linear subspaces, not partitions. The cost is multimodal, with every local optimum kept. The criterion is closure, not locality or informativeness about a far environment. | Proposed |
| THEORY-258 | Optimizing a language model on feedback from a simulated population in which a few users reward harmful validation selects a policy that picks those users out by contextual cues and harms only them, with no one designing the targeting | Williams et al. (2024), LIT-1008, §4.2 and Appendix F.2, read in full in NOTE-798. Shown in simulation only, in one environment class (therapy-talk), with the users’ gameability written into the simulated rater’s prompt and harm judged by an LLM. The behaviour targeted is overt validation, which the paper also calls extreme sycophancy; the covert behaviours (lying, omission) were not tested against a small minority. It is a case of influence fixed by selection, not a finding that anyone was manipulated. | Proposed |
| THEORY-259 v2 | For a recursive family of likelihoods and the universal prior, the Bayesian two-part code length −log Pr(D|H) − log m(H) equals the ideal-MDL length K(D|H) + K(H) plus the randomness deficiency of D for H, up to a constant fixed by the family; so ideal MDL and MAP selection agree to within a constant among hypotheses for which the data are random, and can part where they are not | Vitányi & Li (1999/2000), LIT-225, read in NOTE-801. With the universal prior m and a recursive family Pr(·|·), −log Pr(D|H) − log m(H) = K(D|H) + K(H) + d(D|H) + O(1), where d(D|H) = log(m(D|H)/Pr(D|H)) is the universal randomness deficiency of D for H; d ≥ −K(Pr(·|·)) − O(1), and d is bounded exactly when D is Martin-Löf random for H. So ideal MDL and MAP agree to within a constant on admissible hypotheses (Theorems 3–5, re-derived by the record) and part where the data are not random for the hypothesis (0ⁿ against the fair coin). The paper’s slack α = K(Pr(·|H)) + K(P) is an upper bound, not the gap. | Active |
| THEORY-260 v3 | An individual string’s information splits non-trivially into structure and noise only in a model class without a universal member: with partial recursive models every string’s minimal sufficient statistic is trivial, while with total recursive functions it is not, and the finite-set, computable-distribution and total-function classes agree to within logarithmic terms | Vitányi (2001/2006), LIT-229, read in NOTE-790. Sophistication, the shortest model that completes an optimal two-part code, is =⁺ 0 for every string if partial recursive models are allowed (Lemma 6.2). With total recursive models it ranges from about 0 for random strings to above n − log n − 2 log log n for some string of every length (Theorem 6.5), and it agrees with the finite-set and probabilistic versions to within O(log n) (Lemmas 7.1–7.2). It is not computable, and a sufficient-statistic oracle would compute K (Theorems 8.1, 8.3). It says nothing about any computable or learned model. | Active |
| THEORY-261 v2 | In sparse distributed memory, recall of uniform random data from exact cues is a signal-to-noise problem whose optimum activates about (2MT)^-1/3 of the hard locations, and capacity then grows in proportion to the number of hard locations, rising toward about a tenth of them at 0.999 bit fidelity, not with the word length | Kanerva (1992), LIT-921, §§3.5–3.7, read in full in NOTE-779, after Jaeckel (1989a). An approximate derivation for uniform random data and exact retrieval cues. It does not cover noisy cues, which lower capacity, or clustered data, which the uniform design handles badly, and it does not contain the critical-distance analysis that is sometimes attributed to it. | Active |
| THEORY-262 | Neural complexity is low when a system’s parts are independent or uniformly dependent and high when small subsets are nearly independent while large ones are integrated; in simulated cortex, patchy grouped connectivity raises it above random connectivity of equal density | Tononi, Sporns & Edelman (1994), LIT-998, read in NOTE-767. C_N, the summed shortfall of average subset integration below a linear rise with subset size, is shown low at both extremes for one family of Gaussian matrices, and higher for patchy than for uniform wiring in one simulated visual area and in small linear systems. All of it is simulation. It is a whole-system number over fixed components: it does not find units or boundaries. | Proposed |
| THEORY-263 v2 | A coding rate that varies with the realised sample and output makes rate-distortion generalisation bounds data-dependent, and with the rate set to the pointwise information density log dP_{W|S}/dP(W) against a fixed prior the bound is the disintegrated PAC-Bayes bound | Sefidgaran & Zaidi (2023; IEEE Trans. Inf. Theory 2024), LIT-233, read in NOTE-806. Theorem 1: with a sample-dependent rate R_{S,W}, gen ≤ √(4σ²(R_{S,W} + log(√(2n)/δ))/(2n−1) + ε). With R_{S,W} = log dP_{W|S}/dP(W) the coding condition holds at ε = 0 and the bound is the disintegrated PAC-Bayes bound. The general Theorems 3–5 recover Rivasplata et al.’s PAC-Bayes bound and Xu–Raginsky’s. The coding construction is proved for finite alphabets only. The general proofs are change of measure. The rate is a Shannon code-length difference against a prior, not Kolmogorov complexity. | Active |
| THEORY-264 | A task given by demonstrations and the same task given by an instruction are carried in a language model by mostly different attention heads, so function vectors find no common task representation across the two presentations | Davidson et al. (NeurIPS 2025), LIT-942, read in NOTE-803: 4 to 7 of the top 20 function-vector heads are shared between the two forms in twelve Llama and OLMo models, the two vectors add, and swapping heads and activations between them costs accuracy. Kirsanov et al. (2025), LIT-946, read in NOTE-789, find the same split in representational geometry. Neither shows that no common representation exists, only that these methods find none; neither varies a pragmatic frame. | Proposed |
| THEORY-265 v2 | In Tissot et al.’s minimal model of bistable deciders in a modular coordination game (thirty modules of ten, couplings 1 within modules and 0.01 across), phase synchronisation within modules, driven only by each unit’s local payoff, makes each module respond to the others as a single unit, and synchrony matched to the modules is needed: global synchrony does not | Tissot, Levin, Buckley & Watson (2024), LIT-989, read in full (v1 and v2) in NOTE-773. In a simulated game of 30 modules of 10 units, each unit shifts the phase of its decision cycle toward partners it currently agrees with. Phases synchronise within modules, each module then switches as a block, and 50 of 50 runs with the learned phases reach a global optimum against 0 of 50 without; imposed global synchrony does not help. It is one clean game, one parameter setting, and a postulated phase rule; the modules are built in, and timing finds them rather than drawing them. Re-implemented by the sixteenth status review: learned phases, and module-matched phases imposed by hand, reach the optimum; random, shuffled and global phases do not make modules respond as units. The effect matters only where modules are isolated enough to lock in. | Active |
| THEORY-266 v2 | For a loss in [0, 1] that is L-Lipschitz in a distortion, with probability at least 1 − δ the average generalisation error along an optimisation trajectory is bounded, under a square root, by the rate-distortion function of the trajectory’s law given the sample, a coupling term that carries the trajectory’s dependence on the sample, and a distortion term 4Lε | Sefidgaran & Zaidi (2023), LIT-233, Theorem 7, read in NOTE-806. For an L-Lipschitz loss in [0, 1], with probability ≥ 1 − δ, the mean of gen(S, W^t) over iterations is at most √((RD(S, ε; π_S) + log(√(2n)M/δ))/(2n − 1) + 4Lε). RD is computed for the sample at hand. The coupling coefficient M depends on the unknown distribution and absorbs I(W^T; S). The CIFAR-10 experiment drops M and 4Lε and shows only that the estimated rate and the test gap fall together over learning rates. For FCN4 the plotted rate term is about 3, which is vacuous for 0–1 loss. | Active |
| THEORY-267 v3 | In Rasooly and Rozzi’s pre-registered randomised experiment on 817 Manifold play-money markets, about 59% of a ±5-point price shock that no trader’s information supported was still present after 60 days in unresolved markets, with about 25% undone in the first week and reversion slowing after it; their model of finitely many risk-averse traders gives such partial, slowing reversion even with no learning, and the data cannot tell that from learning | Rasooly and Rozzi (2025), LIT-958, read in full in NOTE-778. A pre-registered field experiment on 817 Manifold markets found about 59% of a random ±5-point shock still present after 60 days in unresolved markets. Reversion was 25% in week one and 6% more over the next three weeks. The paper’s model gets partial persistence from finite, risk-averse traders even with no learning. The data cannot say whether traders came to believe the shocked price. Its evidence that more traders or an outside estimate reduce persistence is correlational and weak. | Active |
| THEORY-268 | An emergence measure averaged over a system’s transitions can be positive while its local value is negative at particular transitions, so emergence so measured belongs to the ensemble, not to each moment | Varley (2022), LIT-953, read in full in NOTE-756. Both the coarse-graining and the ΦID accounts of emergence score an expected past–future mutual information, whose pointwise values can be negative. In one constructed toy, about 53% of informative micro transitions map to misinformative macro ones, and the synergy atom is negative for 31.25% of transitions, while both averages are positive. The paper argues the possibility is general and shows it in instances; it does not show that every system flickers, or say what a negative moment means. | Proposed |
| THEORY-269 v2 | In OLMo-1B, OLMo-7B and GPT-J, how well an affine map from subject to object representation reproduces a factual relation (its LRE causality) tracks how often the relation’s subjects and objects co-occur in pretraining, with mean causality above 0.9 beyond about 4.4k, 2.0k and 1.1k co-occurrences respectively, and, across OLMo-7B’s eight checkpoints, at whatever step that count is reached | Merullo, Smith, Wiegreffe and Elazar (2025), LIT-972, read in full in NOTE-786. 24 factual relations, three models, eight OLMo-7B checkpoints; r = 0.82 between LRE causality and mean subject–object co-occurrence, above either term’s frequency alone. Correlational by the authors’ own statement. The linear objects are per-relation affine maps between hidden states, not attribute directions. | Active |
| THEORY-270 v3 | In Goldwasser, Gruber, Kalai and Paradise’s common-nonsense model, where the source language and the plausibility prior are uniform over sets from which shared random nonsense is removed and translators are one-to-one, maximum likelihood with the prior alone translates without parallel data with error O(log|Θ| / (α·min(m, |T|))) with high probability, falling in the shared nonsense α, in the size of the source language and in the number of samples | Goldwasser, Gruber, Kalai and Paradise (NeurIPS 2023), LIT-941, read in NOTE-804. Proved for maximum likelihood in stylised random models with uniform languages and one-to-one translators; in one model the bound O(log|Θ| / (α·min(m,|T|))) is tight up to a constant. Information- theoretic only. The prior substitutes for parallel data in learning the decoder, not for information in a message. | Active |
| THEORY-271 v2 | In a toy subject–verb–object corpus whose eight subjects carry every combination of three binary aspects, the subjects’ raw co-occurrence rows form a parallelepiped if and only if, for each object, its four sentences are equally probable; any other sentence distribution breaks it | Torii, Maeda and Hidaka (2024), LIT-977, Theorem 1 (§5.5), read in full in NOTE-781. Necessity is sound and short. The case analysis over permutations, and sufficiency, are loosely written. Exact shapes, raw counts, one design, and independent aspects that make the concept lattice Boolean. It says nothing about the logarithm or PMI, about noisy or approximate shapes, or about attributes that imply one another. | Active |
| THEORY-272 v3 | In Hopfield’s 1982 simulations at N = 30 and 100, a network of threshold units with symmetric Hebbian couplings acts as a content-addressable memory whose stored random patterns are attractors: recall degrades severely near 0.15N patterns, a pattern placed 10 bits from another at N = 100 often fuses with it, and at 25-fold overload no stored pattern stays stable | Hopfield (1982), LIT-918, read in full in NOTE-819. The energy descent is derived for symmetric couplings; everything quantitative, including the 0.15N figure, the basin width and the merging distance, is simulation at N = 30 and 100. It does not say that spurious states come only from overload: they appear at a low load too. Nor does it say anything about addressed memory. | Active |
| THEORY-273 v2 | Inductive and explanatory usefulness is necessary but not sufficient for a natural kind: it holds of classes that share any natural property, and on its own it cannot tell a natural kind from a conventional or pragmatic one | Bird and Tobin, SEP “Natural Kinds” (2008; rev. 2022), LIT-244, read in full in NOTE-769: §1.1.1’s criteria, §1.2.1 on induction over properties and relations, and §3’s report of Lemeire (2018). The necessity half is common ground; the insufficiency rests on counterexamples and, for the step to conventional kinds, on a reported argument. It does not say what does suffice, and it does not deny that usefulness is evidence. | Proposed |
| THEORY-274 | Sequence models trained only on a graph’s edge bigrams store it as a global embedding geometry, not as a lookup, although the lookup is expressible, found faster and no less succinct; in a wide two-layer weight-tied model the geometry is the top Laplacian eigenspace, reached by cross-entropy training without a rank bottleneck, regularization or multi-hop supervision | Noroozizadeh, Nagarajan, Rosenfeld & Kumar (2025), LIT-995, read in NOTE-800. Empirical throughout: path-star graphs up to 5×10⁴ nodes, four tiny graphs, frozen-embedding controls; the two-layer spectral analysis is informal and rests on an unproved observation (App. F). It does not explain why deeper models prefer the geometry, which the paper poses as open, and its main transformer runs used weight decay. | Proposed |
| THEORY-275 v5 | In two optically trapped beads with a symmetric hydrodynamic coupling, one trap moved by a recorded noise drive, time-delayed mutual information and transfer entropy follow the drive’s path rather than the coupling’s symmetry: the flow between the beads reads two-way under moderate drive, in experiment and numerics, and one-way under strong drive, in numerics of the fitted model only | Das, Manikandan and Banerjee (2025), LIT-947, read in NOTE-788. Two colloids are coupled by the fluid through a symmetric tensor, and recorded noise moves one trap. Time-delayed mutual information and transfer entropy give drive → driven → other, with backflow at moderate drive. In numerics only, flow is one-way at strong drive. With no drive the coupled particles are independent at steady state. The paper does not test an unrecorded drive shared by both units, and it does not claim that the measures reveal coupling architecture. Whether the same holds in other reciprocally coupled systems is QUESTION-186. | Active |
| THEORY-276 v2 | In a network of identical units with identical couplings, the orbits of the graph’s symmetry group are synchronization clusters, and a cluster moved only by its own factor of the group can lose synchrony while the others keep it | Pecora et al. (2014), LIT-960, read in NOTE-775: eq. (1), the IRR block-diagonalization (eqs. 2–4, 7), the derivation of isolated desynchronization (eq. 6) and an 11-node electro-optic experiment. The pattern of clusters that can synchronize is read from the wiring; whether each does is set by the dynamics through its own transverse block. Symmetry is sufficient, not necessary, for clusters. The paper says nothing about external drive, so the use of these clusters as a sign of coupling rather than a shared cue is the record’s inference. | Active |
| THEORY-277 v2 | For individual data, at every bound on model complexity, the model with the shortest two-part code is, to within O(log n), the best-fitting model in randomness deficiency, although the fit itself cannot be computed or approximated | Vereshchagin & Vitányi (2002/2004), LIT-239, read in NOTE-787, Theorem IV.8: β_x(α) + K(x) and λ_x(α) agree to within O(log n) for a string of length n. Every set minimising K(S) + log |S| at complexity α is within O(log n) of the best fit there. h_x and λ_x are upper semicomputable, while β_x is not semicomputable. Restated by Grünwald & Vitányi, LIT-224, §6.2. Finite-set models; computable distributions at O(log n) cost. It says nothing at the (k/2) log n scale of parametric model selection, and nothing about K(A) + K(x | A). | Proposed |
| THEORY-278 v3 | Under MSE loss, in Han, Papyan and Donoho’s VGG, ResNet and DenseNet runs on five balanced ten-class datasets, the trained classifier stays near the least-squares classifier for its own features from an early epoch; and on that central path, for unconstrained features continually renormalized to identity within-class covariance and without weight decay, gradient flow drives the class-separation singular values to infinity at equal rates, which in that model is neural collapse | Han, Papyan & Donoho (2021), LIT-974, read in NOTE-783. MSE loss splits exactly into a least-squares term and a non-negative deviation term, and the deviation becomes negligible early in training in 15 dataset–network cells. On that central path, with λ = 0, the loss is ½ Σ 1/(ω_j² + C) in the singular values of Σ_W^(−1/2)M̃. Under a flow that re-whitens the features after every step, each ω_j grows as (4t/N)^(1/4), and their ratios tend to 1. That is NC1 and NC2, and NC3–NC4 follow. Not shown: that ordinary training is this flow, or anything for cross-entropy or with weight decay. | Active |
| THEORY-279 v2 | Early in training, image classifiers and language models act on the low-order statistics of their inputs, first-order before second-order, and later lose that sensitivity as they come to use higher-order structure | Belrose et al. (2024, ICML), LIT-952, read in NOTE-777. Over training, ConvNeXt V2, Swin V2 and RegNet-Y on five small image datasets are probed with images whose class means or covariances are grafted from another class, and with maximum-entropy samples that keep only those statistics. Accuracy on these rises and then falls, often below chance. Pythia fits unigram-sampled text before bigram-sampled text. The ordering is empirical and covers orders one and two. The Taylor argument that motivates it is a heuristic, and the paper does not measure an ordered sequence beyond second order. | Proposed |
| THEORY-280 v2 | The bisimulation metric between two finite Markov chains with observed states and a known cost bounded by 1 can be estimated without a transition model from independent samples of each chain’s discounted state-pair occupancy, to accuracy ε with probability 1 − δ from a number of samples polynomial in the state-space sizes, 1/(1−γ), log(1/δ) and 1/ε² | Calo, Jonsson, Neu, Schwartz & Segovia-Aguas (2025), LIT-948, read in NOTE-763. Bicausal occupancy couplings are characterised by constraints that use only each chain’s sampled occupancy measure over consecutive state pairs. A stochastic primal-dual method on them gets an ε-accurate estimate with probability 1−δ from O((|X||Y|(|X|+|Y|) + (|X|+|Y|)log(1/δ))/((1−γ)²ε²)) independent samples per chain. The states must be observed and enumerable, the cost known, and the samples drawn with restarts. A single running stream and latent states are outside it. | Active |
| THEORY-281 v2 | Perfect concept erasure caps what a representation can keep at the information not about the concept: for X of finite support, if Z is independent of A then I(Z;X) is at most H(X|A), and a deterministic erasure reaches that cap only when the concept groups’ distributions are permutations of one another | Chowdhury et al. (2025), LIT-963, read in full in NOTE-820. The cap (Lemma 3.3) is a two-line chain-rule argument that needs only the Markov condition A → X → Z. The permutation condition is proved necessary and sufficient for deterministic maps (Appendices A.3 and A.4), with finite supports and disjoint groups. The paper’s further statement, that the cap cannot be reached when the groups are not permutations, is false for stochastic maps, which reach it for any finite distributions with disjoint supports. | Active |
| THEORY-282 v2 | A subspace intervention can reproduce the output effect of changing a variable without localizing it, by pairing a direction that varies with the variable but cannot reach the output with one that can reach the output but does not vary on the data | Makelov, Lange and Nanda (2023), LIT-968, read in NOTE-782. Proved for the construction (§3.2, Lemma A.1); shown in GPT-2 Small’s MLP8 on IOI (46.7% FLDD, falling to 13.5% without the null-space component, 4.2% interchange accuracy) and in GPT2-XL MLPs on factual recall, where a residual-stream direction passes the same test. It does not say that subspace patching is unreliable in general, nor that a found direction with a null-space component is spurious: in a one-dimensional readout the test passes both kinds. The reply (LIT-961) contests the label, not the measurements. | Active |
| THEORY-283 v2 | For a hierarchical multi-index target with isotropic Gaussian inputs and even, separable links, direction k becomes weakly recoverable by the Bayes-optimal estimator at a sample count proportional to its squared weight to the power minus one, so features emerge one at a time through sharp spectral transitions in the number of samples; a target-agnostic spectral estimator attains the thresholds and the optimal weighted error, and a two-layer network whose first layer is that estimator, with a ridge readout, attains them in excess risk | Defilippis, Krzakala, Loureiro and Maillard (2026), LIT-940, read in NOTE-805. Take x ~ N(0, I/d), n = αd, and f⋆ = Σ a_k g_k(⟨w_k, x⟩) with even links of generative exponent two and a_k ~ k^(−γ). Direction k is weakly recoverable at α_k = Θ(a_k^(−2)) (Thm. 3.2). The optimal weighted error is Θ(α^(−1+1/(2γ))) until α ≍ m⋆^(2γ). The spectral estimator on Σ T(y_i)x_ix_iᵀ attains both (Thm. 3.6). The cascade is in the number of samples, not in training time. The network result is for a spectral first layer plus a ridge readout, not gradient descent. | Active |
| THEORY-284 v2 | If a feature’s values form a compact metric space carried continuously and injectively onto the unit sphere, and cosine similarity is locally a C² decreasing function of squared feature distance, then every path on the representation manifold is √(−2g′(0)) times as long as the feature path it images, so on-manifold shortest paths recover the feature’s intrinsic length metric up to one scale; a homeomorphism alone does not fix it | Modell, Rubin-Delanchy & Whiteley (2025), LIT-935, Theorem 1, read in NOTE-802. Under Hypothesis 1 (continuous injective ϕ_f from a compact feature space to the sphere) and Hypothesis 2 (CosSim = g(d²) locally, g ∈ C², g′(0) < 0), path lengths scale by √(−2g′(0)). So geodesics on the representation measure the feature, without knowing g. Both hypotheses are assumed, not derived from training. GPT-2’s years are homeomorphic to both a linear and a logarithmic scale, and only the metric test told them apart. | Active |
| THEORY-285 v2 | In an illustrative active-inference simulation of post-traumatic context inference, run once per phenotype, a prior that one is in a harmful context, made overly precise by a run of harmful trials under the “vulnerable” learning and forgetting weights, makes exploratory sampling look uninformative, so the agent attenuates the periphery, never receives the evidence that would correct the prior, and the belief sustains itself; lowering precision makes the attenuation policy less vigorous without correcting the prior, and the policy returns when precision is restored | Linson, Anderson, Markham, Friston & Moutoussis (2025), LIT-983, read in version 2 in NOTE-766. A mechanism shown in illustrative simulation: policy selection by expected information gain, plus a confident prior, withholds the only disambiguating observations, so the prior keeps itself up. Exposure that restores sampling rebalances it; a precision-lowering drug only suppresses symptoms. No data are fitted, parameters are unreported, and the two intervention arms differ in environment as well as mechanism. | Active |
| THEORY-286 v2 | Under class imbalance the last-layer geometry that unregularized cross-entropy prefers is not the simplex ETF but simplex-encoded-label interpolation: the logits equal the simplex-encoded labels, the classifier and embedding Gram matrices come from that matrix’s SVD, any finite weight decay changes the geometry, and training approaches it more slowly as imbalance grows | Thrampoulidis et al. (2022), LIT-994, read in NOTE-764. For the unconstrained-features max-margin problem under STEP imbalance, every solution has logits ŴᵀĤ = Ẑ (one-hot minus 1/k), ĤᵀĤ = UΛUᵀ and ŴᵀŴ = VΛVᵀ from Ẑ’s SVD (Theorem 1). This is the ETF only if the data are balanced or binary. No finite ridge gives it under imbalance (Proposition 1), though the ridge path tends to it (Proposition 2). ResNet-18 and VGG-13 runs sit closer to SELI than to the ETF, and approach it more slowly at larger R. Not shown: that gradient descent reaches it, and anything with more than one seed. | Proposed |
| THEORY-287 | Internal variables located by interchange intervention as mediating a language model’s in-distribution behaviour predict whether its outputs stay correct under shifts that keep the task’s mechanism better than output confidence or probes of the rest of the representation | Huang, Tao, Icard, Yang and Potts (2025), LIT-987, read in NOTE-765. In Llama-3-8B-Instruct over five tasks and ten shifts, counterfactual simulation is best on 8 of 10; a probe of the located variable beats a probe of its orthogonal complement on 7 of 10. Interchange accuracy and predictive power rise together only until accuracy nears 1. It does not say that the located variables are constitutive, that causal features always win, or anything about shifts that change the mechanism. | Proposed |
| THEORY-288 v2 | In small CIFAR and MNIST autoencoders whose only basis-privileging primitive is the activation function, elementwise tanh and Leaky-ReLU concentrate latent representations into narrow beams arranged by the activation’s discrete symmetry group, even in layers no activation precedes, while their orthogonally equivariant radial counterparts leave them spread, so axis-aligned discreteness there comes from the primitive, not the task | Bird (2025, v4 2026), LIT-976, read in NOTE-759. Autoencoders of width 12–32 and up to three hidden blocks on CIFAR and MNIST, with rotation-equivariant affine maps, initialisation and optimiser. Elementwise tanh (B_n) and Leaky-ReLU (S_n) give beams along or against the basis, or on the ±1 diagonal, and radial tanh and Leaky-ReLU (O(n)) do not. The evidence is density plots, five seeds a condition, with no statistic. The downstream claims, that this causes grandmother neurons, superposition and neural collapse, are untested. | Proposed |
| THEORY-289 v2 | For ordinary least squares on T ≥ d + 2 isotropic Gaussian covariates reused every round, with each round’s labels generated by the previous fit, keeping every earlier round’s data keeps the expected excess test error below π²/6 times the first fit’s, though it rises every round, where replacing the data makes it grow linearly in the number of rounds | Gerstgrasser, Schaeffer, Dey et al. (2024), LIT-971, read in NOTE-815, Theorems 1–2 extending Dohmatob et al.’s replace result. Proved for ridgeless OLS with isotropic Gaussian features, the real covariates reused every round and only labels regenerated. The error is bounded, not constant: it rises every round towards its limit, and every model remains a noisier copy of the first. Small language and diffusion models behave alike over five to eight rounds; a VAE’s error still rises. | Active |
| THEORY-290 v2 | In a two-debater, three-proposition model of deductive debate whose payoff trades true beliefs against changes of mind, the most truth-conducive equilibrium can fall short of the truth-optimal profile because one debater free-rides on the other’s belief-disrupting arguments, and in a narrow band of mixed equilibria a higher weight on truth gives lower equilibrium accuracy | Handfield, Garcia, Hilbe and Yeo (2025), LIT-966, read in full in NOTE-795. With payoff w·v − d (true beliefs against changes of mind), debate between two deductive reasoners is a cooperative dilemma at low and moderate truth weights. Typically one argues boldly and the other free-rides (a snowdrift), and at low weights both exit. A small dip in accuracy as w rises occurs in a narrow band of mixed equilibria. It is shown numerically for two players and three propositions. It concerns collective accuracy, not a belief the pair settles on, and at high truth weight in short debates there is no dilemma. The title claims the model only; groups and richer strategies are QUESTION-173. | Active |
| THEORY-291 | The brain’s visceromotor and interoceptive regions form one intrinsic system that reproduces their tract-traced anatomy and contains the hubs of the default-mode and salience networks | Theriault et al. (2025), LIT-996, read in full in NOTE-761, reporting the group’s own 3 T (N = 550) and 7 T (N = 90) studies; Barrett (2017), LIT-542, read in NOTE-434, for the 3 T system. The anatomy and overlap are reported second-hand. The reading the paper adds, that the named networks’ psychological labels are “destined to fail” and that the brain’s primary function is allostasis, is not part of this account; the authors themselves do not claim allostasis-first is correct. | Proposed |
| THEORY-292 | In CNN image classifiers, concept directions fitted one concept at a time align for attributes that co-occur in the labels, yet a joint fit finds mutually orthogonal directions that still separate each concept with little loss of AUROC, so the alignment is a property of the separate fits and not forced by the representation | Erogullari, Lapuschkin, Samek and Pahde (2025), LIT-937, read in full in NOTE-816. Shown at the last convolutional layer of VGG16 and ResNet18 on CelebA (natural correlations) and FunnyBirds (an injected 70% beak–tail correlation). AUROC is “largely preserved” by the paper’s account, with no values in the text and no error bars. It does not say the model’s own axes are orthogonal, and it says nothing about attributes that imply one another. | Proposed |
| THEORY-293 v3 | For an optimal capacity-bounded learner on an orthogonal mixture of equally frequent random facts and a second domain, the facts are learned not at all below a capacity threshold set by the mixing ratio and in full once capacity exceeds it by the facts’ total entropy, and Pythia models trained on synthetic biographies mixed into web text show a threshold in model size and in mixing ratio | Gu, Lyu, Li and Zhang (2025), LIT-984, read in NOTE-796. Proved for an idealised learner whose capacity is mutual information with the data (Theorem 4.3), on an orthogonal mixture of uniform facts and a second domain; seen in Pythia models from 14M to 6.9B on synthetic biographies mixed into web text. The theory is static. It does not say when in training the facts arrive, and it does not show that SGD reaches the optimal allocation. | Active |
| THEORY-294 v3 | For a wide two-layer ReLU network with zero bias on one-dimensional data whose two classes lie on opposite sides of the origin, the tangent kernel is a constant multiple of the initialization kernel, so lazy training leaves the within-class variability of its features, NC1, where initialization put it | Kothapalli & Tirer (2024), LIT-985, read in NOTE-774. NC1 = tr Σ_W / tr Σ_B of kernel-defined features is a ratio of linear functionals of the kernel matrix (Theorem 4.1). For one-dimensional data, two classes on opposite sides of the origin and zero bias, the ReLU tangent kernel of a wide two-layer net is a constant multiple of the NNGP kernel, so NC1 is the same (Theorem 5.1, re-derived). In higher dimensions it is measured no lower, and for ReLU higher; whether lazy training leaves NC1 in place there is QUESTION-192. The inference that collapse requires feature learning is the reading’s, not proved. | Active |
| THEORY-295 v3 | In a community whose consensus model is replaced whenever a single sound pairwise model comparison favours the challenger, which models get proposed can hold the consensus on a false model while results reproduce almost perfectly, so reproducibility need not track convergence to truth | Devezer, Nardin, Baumgaertner and Buzbas (2019), LIT-988, read in full in NOTE-792. In a Markov-chain and agent-based model where each step tests one proposed linear model against the consensus by AIC or SC, replication cannot change the transition matrix. A boundary-testing population reproduces almost perfectly while rarely holding the true model, and correlations between reproducibility and truth depend on the strategy mix. The consensus is memoryless, scientists hold no beliefs, and an equal strategy mix is shown only never to be the worst, not best. | Active |
| THEORY-296 v2 | In a preregistered multimodal test with clearly seen images, category-selective posterior cortex showed no sustained content-specific synchronization with early visual cortex, which iEEG sampled with 12 electrodes: the preregistered phase coupling was brief, low-frequency and mostly stimulus-evoked, and exploratory amplitude coupling, gamma included, was also brief | Cogitate Consortium, Ferrante et al. (2025), LIT-973, read in NOTE-812. IIT’s proponents predicted sustained gamma-band synchronization between category-selective cortex and V1/V2 throughout a conscious percept. iEEG and MEG phase consistency found only early, brief, 2–25 Hz coupling, mostly evoked, with Bayesian support for the null; exploratory amplitude coupling was also brief. V1/V2 was sparsely sampled in iEEG. It tests IIT’s proposed implementation, not integrated information. | Active |
| THEORY-297 v2 | A bijection between shapes is equivalent, up to null sets, to the linear operator it induces on functions; in orthonormal bases a volume-preserving bijection’s matrix is orthogonal, and an isometry’s commutes with the Laplace–Beltrami operator, so it maps each eigenspace to the matching eigenspace | Ovsjanikov, Ben-Chen, Solomon, Butscher & Guibas (2012), LIT-993, Remarks 4.1–4.3, Theorem 5.1 with App. A, and §5.1, read in NOTE-822. Orthogonality was checked; commutation with the Laplacian is cited as well known. All of it assumes a bijection. The operator runs between two different spaces, but the paper gives no structure for a non-invertible or one-way map, and the stability of truncated eigenspaces is cited to Kato, not shown. | Active |
| THEORY-298 | Report-based evidence cannot test whether posterior cortex suffices for experience, because report itself needs anterior activity, and no marker that bypasses report has a validation resting neither on introspection nor on a contested theory | Seth & Bayne (2022), LIT-982, “Evaluating theories of consciousness” and Box 3, read in NOTE-849 from the accepted manuscript. An argument in a review, not a result: the verification of posterior-sufficiency predictions “relies on subjective report …, which in turn requires anterior cortical activity”, and validating a non-report marker by theory borrows a contested theory, by introspection, unreliable report. It says the methods are lacking “at present”, not that the question is unanswerable. | Proposed |
| THEORY-299 v2 | Structured and translational knowledge-graph embeddings are 0-cochains of a cellular sheaf of vector spaces pulled back from the schema, each triple scored by a norm of the coboundary on its edge and, in the squared-Euclidean form, the whole graph by the sheaf Laplacian; since the zero cochain is always a global section, what they learn is a contrastive margin, not the existence of a section | Gebhart, Hansen and Schrater (2021; AISTATS 2023), LIT-232, §4 and Appendices A and C, read in NOTE-843. A direct identification, covering Structured Embedding, the Unstructured Model, TransE, TransR and RotatE and not bilinear models. That existence of a section is trivial here, and that the only gluing question is whether fixed data extend, is the paper’s own remark taken further by the record; it is what separates this use of sheaves from the contextuality line. | Active |
| THEORY-300 | Acting on a coercive instruction reduces the implicit sense of agency over the outcome, compared with freely choosing the same action | Haggard (2017), LIT-1009, manuscript pp. 16–17 and Fig. 5, read in full in NOTE-827, reporting one experiment by his group (Caspar et al. 2016). Under an experimenter’s instruction to press the key that shocked a co-participant, the perceived action–tone interval was longer and the auditory N1 to the tone smaller than under free choice. It shows a reduced experience of agency, not reduced responsibility, and the review says so. | Proposed |
| THEORY-301 v2 | The Procrustes distance between regularization-normalized representations and their average linear-decoding distance bound each other only through the participation ratio of the kernel difference: a small Procrustes distance forces a small decoding distance, but not conversely | Harvey, Lipshutz & Williams (2024), LIT-257, Proposition 3 and App. A.1, read in NOTE-834. With K_X = XG(X)⁻¹Xᵀ/M, α = Tr K_X, β = Tr K_Y and R_Δ the participation ratio of K_X − K_Y, P⁴/R_Δ ≤ E‖Xw* − Yv*‖² ≤ (2(α + β)P² − P⁴)/R_Δ for targets with E[zzᵀ] = I. The Procrustes–Bures equivalence is imported from LIT-250. Kernels with orthogonal supports show the converse fails: Procrustes distance maximal, decoding distance as small as 2/r. Finite samples, linear readouts only. | Active |
| THEORY-302 | Coordinated action is controlled by tuning relatively autonomous coordinative structures, not by commanding muscles: a higher level specifies an equivalence class of acceptable states and sets the parameters of self-regulating units, leaving the realized details to them | Turvey (1977; read in the 1975 Haskins report), LIT-904, read in NOTE-826. Argued from Bernstein’s degrees-of-freedom problem and Greene’s equivalence classes, and supported at the spinal level by reflex-probe studies showing the segmental apparatus retuned in the tens of milliseconds before voluntary movement, and by Fel’dman’s joint that goes to a preset equilibrium whatever its initial conditions. Its extension to all levels, and to tuning set directly by vision, is the author’s speculation. | Proposed |
| THEORY-303 | A measurement scenario whose compatibility hypergraph is acyclic admits no contextuality: locally consistent context distributions always glue to a global one, so a contextual scenario needs an induced cycle of length at least four | Vorob’ev (1962), as stated in Budroni, Cabello, Gühne, Kleinmann & Larsson (2022), LIT-263, §V.B.2, Eq. 79, and App. A.6, read in NOTE-844. Distributions that agree on overlaps and sit on a hypergraph with the running-intersection property glue, step by step, to one joint distribution. For sharp measurements this means a chordal compatibility graph. So CHSH’s square and KCBS’s pentagon are the smallest contextual scenarios. Stated and illustrated in the review, not proved there. | Proposed |
| THEORY-304 v3 | In plane Couette and Poiseuille flow, measured in the energy norm, the linearized operator is so far from normal that perturbations can grow transiently by O(R) and resonate by O(R²), and operator perturbations of size O(R⁻²) make it eigenvalue-unstable, at Reynolds numbers where eigenvalue analysis predicts stability | Trefethen, Trefethen, Reddy & Driscoll (1993), LIT-932, read in NOTE-839: computed scalings for the linearized shear flows, mostly credited to earlier work and unified through pseudospectra. That transition to turbulence happens by this linear growth plus nonlinear mixing is the paper’s conjecture from a 2 × 2 model, and is not part of this account. | Active |
| THEORY-305 v2 | SimCLR’s InfoNCE loss, over all n objects with a Gaussian kernel on the unit sphere, equals a graph-Laplacian quadratic form on the augmentation matrix plus the log of InfoNCE’s normalizers, which is spectral clustering only in a sense that admits any regularizer and does not make the minimizer the Laplacian’s eigenvectors | Tan, Zhang, Yang & Yuan (2023, ICLR 2024), LIT-227, read in NOTE-846: Theorem 3.1 and its proof (App. A), Lemma 2.5 and Definition 2.7. The identity between objectives is exact on a finite object set with symmetric π. The paper’s “spectral clustering” is any Laplacian form plus any regularizer; it names no minimizer and no population optimum, so it supports neither an eigenvector reading of InfoNCE nor the density-ratio optimum of THEORY-001. | Active |
| THEORY-306 v3 | MSN’s objective penalizes unequal cluster sizes explicitly and SwAV’s enforces equal sizes, and in one study with mini-batches of two to eight ImageNet classes, SimCLR, MSN and VICReg lost 11 to 18 points of ImageNet linear accuracy while MAE and data2vec lost under one | Assran et al. (2022), LIT-231, §§3–5 and Appendix C, read in NOTE-850. The prior is explicit in MSN’s loss (a KL to uniform over mean cluster assignments) and in SwAV’s equipartition constraint. For VICReg it rests on an informal reduction of a simplified loss to K-means and on K-means’s cited tendency to equal clusters, and for SimCLR on a cited equivalence, so the title claims the prior for MSN and SwAV only. The effect is shown with batches of two to eight ImageNet classes, one run per cell, not with natural long tails; the open half is QUESTION-171. | Active |
| THEORY-307 | Adaptation by trial and error in a large system finishes in a practicable time only if partial adaptations are retained, and retention requires that the system not be fully joined: parts must be separated, at least temporarily, by constancies, and where later learning shares parts with earlier learning it destroys it | Ashby (1952; 2nd ed. 1960), LIT-787, read in NOTE-851, Chs. 10–16. If all successes must occur at once, trials grow as (1/p)ᴺ; if each is kept once found, roughly as N/p. Keeping one needs no channel from what is still changing to what is already right, so a fully joined system, the Homeostat included, cannot accumulate; constancies cut a system into independent parts. Exact for the type-cases; the fit to brains is qualitative. | Proposed |
| THEORY-308 v2 | The neural Donsker–Varadhan estimator of mutual information is strongly consistent as an extremum estimator over compact families of critics, and, for critics bounded by M and L-Lipschitz in their d parameters, its uniform deviation from the population bound needs a number of samples set by d, M, L and the parameter radius, not by the data dimension | Belghazi et al. (2018), LIT-256, §3.3 and App. 8.2.2–8.2.3, read in NOTE-828. On a compact domain with Lebesgue densities, the supremum of the Donsker–Varadhan bound over some compact network family is within any η of the mutual information, and the empirical supremum converges to the population one almost surely. Uniform deviation ε needs Õ(d log d/ε²) samples for d parameters, under bounded, Lipschitz critics. The guarantee is for the exact empirical maximizer, not for gradient training. The finite-sample estimate is not a bound (Poole et al., LIT-246), and the proof has two gaps a reading found. | Active |
| THEORY-309 v2 | If contexts are defined by joint measurability alone, every nondisturbing correlation, maximally contextual ones included, is realized by trivial measurements on a one-dimensional quantum system, so Kochen–Specker contextuality needs a stronger operational notion of context | Budroni, Cabello, Gühne, Kleinmann & Larsson (2022), LIT-263, §IV.B.2, Eqs. 27–28, adapting Fritz (2012), read in NOTE-844. For a nonsignalling p(ab|xy), the POVMs G^{xy}_{ab} = p(ab|xy)𝟙 on a one-dimensional space are jointly measurable for each pair and reproduce p. So contextuality relative to joint measurability alone is trivial, and the review requires contexts of repeatable, nondisturbing measurements. Liang, Spekkens & Wiseman’s sharpness parameter is the other known escape. | Active |
| THEORY-310 | On a forward-looking justification of blame, a counterfactual capacity condition calibrated to what makes blaming effective is redundant: fixing its parameters presupposes that blaming such agents is good policy, so freedom is ascribed because of blameworthiness rather than grounding it | Harland (2020), LIT-991, §3, read in NOTE-847. Argued, not shown, against Vargas’s agency cultivation model, whose free-will test sets its similarity and proportion parameters by what is co-optimal for cultivating moral agency. The argument is about that model only, and works class by class. It does not show that freedom is irrelevant to responsibility in general, and Vargas is read here only through Harland’s quotations. | Proposed |
| THEORY-311 v2 | Groupware that requires extra work from members who do not perceive a direct benefit from it, where that work is not made part of their job, is resisted or goes unused, and the applications that succeed in groups without a mandate give each user who does the work a benefit of their own | Grudin (1994), LIT-757, read in NOTE-835. The first of his eight challenges for groupware, argued from cases (meeting schedulers, voice annotation, project management) and from email’s success, where the sender does a little more work and also wants the message read. An argued review, not a measurement, and Grudin himself says that removing the disparity does not guarantee use. | Proposed |
| THEORY-312 v2 | The large-batch InfoNCE loss is the negative HSIC between representations and image identity plus a nonnegative log-mean-exp of the centred critic, so it bounds a kernel dependence loss from above | Li, Pogodin, Sutherland & Gretton (2021), LIT-248, eq. 28 and Theorem B.1, read in NOTE-830. On a finite dataset of N images with one-hot identity labels, the large-batch InfoNCE loss equals −HSIC(Z,Y) + E_Z log E_Z′ exp(k − μ₁) exactly. The second term is nonnegative by Jensen (the record’s step), and for a bounded kernel it is at least γHSIC(Z,Z) less a second-order remainder (Theorem B.1, printed with the remainder’s sign reversed). It does not say InfoNCE is HSIC, and it says nothing of the finite-batch estimator. | Active |
| THEORY-313 v3 | With a kernel normalised to k(x,x) = 1, the covariance operator of a distribution is a density operator, and its quantum relative entropy is a lower bound on the Kullback–Leibler divergence that is tight for every pair of distributions only for an orthonormal, hence discrete, embedding, lies above the KL of the kernel-smoothed distributions, and on the torus, with Fourier coefficients proportional to e^(−σ‖ω‖₁) and strictly positive Lipschitz densities, is within O(σ²) of KL as the bandwidth σ shrinks | Bach (2022), LIT-255, read in NOTE-837. Σ_p = ∫ϕϕ* dp is uncentred and unit-trace, so p ↦ Σ_p maps distributions to quantum states, and D(p̃‖q̃) ≤ D(Σ_p‖Σ_q) ≤ D(p‖q) (Proposition 4(d), Eq. 8). The upper bound is joint convexity, with equality for every pair only if k(x,y) = 0 for x ≠ y. The lower bound is monotonicity under a measurement whose outcome law is p smoothed by h(x,y) = ⟨ϕ(x), Σ^{−1/2}ϕ(y)⟩². The O(σ²) gap is shown only for kernels on the torus with Fourier coefficients proportional to e^(−σ‖ω‖₁), with Lipschitz densities. It does not cover centred kernels, or similarity measures that compare Gram matrices of representations. | Active |
| THEORY-314 v2 | Every minimizer of an arbitrary cost on the training outputs plus a strictly increasing function of the RKHS norm lies in the span of the kernel functions at the training points, by the reproducing property and orthogonal decomposition alone | Schölkopf, Herbrich & Smola (2001), LIT-261, Theorem 1 with its proof (eqs. 18–24), read in NOTE-836 and checked. No convexity of the cost and no Riesz theorem is used; the RKHS is built from the kernel, so the reproducing property holds by construction. The theorem is stated over countable kernel expansions of finite norm, assumes a minimizer exists, and does not cover costs that see f other than through its values at the training points. | Active |
| THEORY-315 v2 | For a state whose four-state reflection orbit is realizable, generalized noncontextuality bounds two binary predictabilities by |⟨X⟩| + |⟨Z⟩| ≤ 1, so the form of a predictability trade-off, not its existence, can witness contextuality | Catani, Leifer, Scala, Schmid and Spekkens (2022), LIT-980, read in NOTE-825. Proved analytically, with a saturating model, for preparation noncontextuality and exact operational equivalence. The bound constrains a whole uncertainty relation only in a theory where every state has the orbit; the qubit’s circle violates it, and a classical theory without the symmetry escapes it. It needs no perfectly distinguishable states, and it is not a sheaf or Kochen–Specker criterion. | Active |
| THEORY-316 v2 | Frankfurt-style cases defeat alternative-possibilities conditions on moral responsibility but leave standing the incompatibilist condition on an action’s causal history, which is the more fundamental one | Pereboom (2001), LIT-1006, Chapter 1 pp. 1–6 and the Introduction (pp. xv), read in NOTE-823, Skimmed. Fischer concedes that a Frankfurt-style case does not refute a requirement that the action not be deterministically produced by factors beyond the agent’s control, and Pereboom builds causal-history incompatibilism on that concession. It does not say that determinism rules out responsibility; that is argued in Chapter 4, which was not read. | Proposed |
| THEORY-317 v3 | Epistemic injustice wrongs a person in her capacity as a knower, testimonially through a hearer’s prejudicially deflated credibility judgement, and hermeneutically through a gap in shared interpretive resources owed to her group’s relative powerlessness, with no hearer’s prejudice required | Fricker (2007), LIT-1004, known here only through her own three-page précis (Theoria 2008), read in NOTE-832, Skimmed. The two definitions and the claim that both are ethical wrongs, not only epistemic dysfunctions. It does not say that every gap in shared concepts is an injustice: on the précis’s terms the gap must be owed to the relative powerlessness of a social group the subject belongs to. | Proposed |
| THEORY-318 v2 | A bound k on the max-information between a dataset and an analyst’s chosen statistic multiplies by at most 2^k the probability that the statistic overfits that dataset, and an ε-differentially private mechanism on datasets of n points keeps k at most log₂e·εn, whatever the distribution on datasets | Dwork, Feldman, Hardt, Pitassi, Reingold & Roth (2015), LIT-964, Supplementary Material only, read in NOTE-848 (Skimmed: the main text was not reached). Theorem 2 and Lemma 5 are proved there and were checked: P[overfit] ≤ 2^{I∞}·max P[overfit], and ε-DP gives I∞ ≤ log₂e·εn. Thresholdout’s guarantee (Theorem 11), n = O(ln(m/β)/τ²·min{B, √(B ln(m/β))/τ}), is stated with its proof elsewhere. Statistical queries on a discrete universe only, and a procedure that prevents inflation, not a correction for a search already run. | Active |
| THEORY-319 v2 | When two views are redundant for a label, the predictor that infers one view from the other is within εX + 2√(εXεZ) + εZ of the Bayes predictor in mean squared error, and it is linear in the contrastive density ratio, so for a bounded label and a square-integrable ratio a linear readout of m random evaluations of the exact ratio approaches it at rate 1/m, with no symmetry between the views required | Tosh, Krishnamurthy & Hsu (2021), LIT-251, read in NOTE-841: Lemma 1, §2.3–2.4, Lemma 2 and Theorem 3. The label enters only through how redundant the views are about it; the representation is the density ratio p(x,z)/(p(x)p(z)), learned without labels. Population level. The error-propagation results need a uniform bound on the ratio, and the low-dimensional direct embeddings are shown to exist, not to be reached. | Active |
| THEORY-320 v2 | In a spectral contrastive graph that joins labelled known classes to unlabelled data, a novel labelling’s linear-probe residual is exactly its part outside the top eigenspace that the labelled rows of the discarded eigenvectors cannot absorb, so which partition of the unlabelled data is discovered depends on the known classes: ones sharing the target’s attribute can remove the residual, and ones sharing a rival attribute can raise it | Sun, Shi, Liang & Li (2023), LIT-235, read in NOTE-833. On the population graph, at the exact rank-k optimum, R(U*, y) = ‖(I − P_{L♭})U♭ᵀy‖² (Theorem 5.5, stated as ≤, proved as = in C.1). In a one-sample-per-kind toy, a known class sharing colour makes a colour labelling recoverable, and one sharing shape makes it worse than none (Lemma 5.4). The general error bound (Theorem 5.6) is approximate and pools all known classes into one block, and is not part of this account. Nothing here is about trained networks. | Proposed |
| THEORY-321 v4 | Under repeated DeGroot averaging in a strongly connected society, the consensus converges to the truth as the society grows if and only if the largest influence weight vanishes, so network structure alone, not the members’ common updating rule, decides whether the group belief is right | Golub & Jackson (2010), LIT-999, Proposition 2 with Lemma 1, Corollary 1, Proposition 3 and Theorem 1, read in NOTE-840 with the main proofs checked. The members are naïve, not sound: they ignore repeated information, and only the first round is Bayesian. The result is in a model with fixed weights, independent signals and n → ∞. Speed of consensus and its correctness are independent. | Active |
| THEORY-322 | The sense of agency over an action’s outcome draws on prospective signals from action selection and outcome prediction, not only on retrospective comparison of outcome with prediction | Haggard (2017), LIT-1009, read in full in NOTE-827. A review, reporting a binding experiment in which action binding tracked the probability of a tone on trials with no tone, a patient study in which that prospective part was absent in schizophrenia, and priming studies in which ease of action selection raised the sense of control over an outcome it did not predict. It does not say the experience is accurate: the prospective part is by its nature blind to whether control was actually exercised. | Proposed |
| THEORY-323 v2 | Under spatially uncorrelated white noise, a stable non-normal linear system holds more variance than the sum of its pole contributions, and equality holds only when the operator is normal, so its spectrum understates the standing variance | Farrell & Ioannou (1996), LIT-931, read in NOTE-831, with Trefethen et al. (1993), LIT-932, read in NOTE-839. Linear algebra, worked in examples: growth over time t is the top singular value of the propagator, which the eigenvalues bound from below, not above. It holds in a chosen norm, and a norm can always be found that makes the operator normal. It says nothing about whether the growth survives nonlinearity. | Proposed |
| THEORY-324 v2 | A system adapts by trial and error to an environment whose effect on its essential variables it does not know only if a second feedback, through those variables, changes the parameters of its primary feedback; and if that feedback changes them whenever, and for as long as, an essential variable is outside its limits, every equilibrium the whole can reach is an adapted one | Ashby (1952; 2nd ed. 1960), LIT-787, read in NOTE-851. Necessity is deduced from the trial-and-error rule against a Black Box environment; sufficiency from the theorem that a whole is at equilibrium only where every part is. The Homeostat shows it in a four-unit linear machine. The parameter changes are blind, and the account says nothing about how long the search takes, which is the subject of THEORY-307. | Active |
| THEORY-325 v2 | Random variation of a linear operator destabilizes it generically, needing less variation the more non-normal and less damped the mean operator | Farrell & Ioannou (1996), Part II, LIT-929, read in NOTE-842. Necessity is a one-line bound and the destabilization is shown in explicit examples. Genericity under noise is cited to stochastic stability theory, and the role of non-normality and damping is shown numerically. In the deterministic examples, variation much faster than the transient growth destabilizes nothing. Since 2026-10-19 the deterministic half is THEORY-724, and this THEORY holds the stochastic half. | Proposed |
| THEORY-326 | Hermeneutical injustice is having a significant area of one’s social experience obscured from collective understanding owing to hermeneutical marginalisation, which may be systematic or incidental, so it does not require that the subject belong to a powerless social group | Fricker (2006), “Powerlessness and Social Interpretation” (LIT-1046, NOTE-859), drawn by her own note from the book’s final chapter, with her 2017 restatement (LIT-1048, NOTE-853). The generic definition covers a systematic case, where marginalisation is persistent and wide-ranging, and an incidental case, a “one-off moment of powerlessness” in a “highly localized patch” of experience, which a socially powerful man can suffer. It does not say that every conceptual gap is an injustice. A gap with no marginalisation behind it, like an undiagnosed illness, is “circumstantial epistemic bad luck”, and the obscured area must be of the subject’s social experience. | Proposed |
| THEORY-327 v2 | Fricker, in her 2003 paper and her 2017 retrospective, holds that testimonial injustice is an ingenuous misjudgement of a speaker’s credibility caused by prejudice, and that deliberate manipulation of credibility is a related but distinct wrong; and she accepts Anderson’s structural form, which is pre-emptive: a speaker’s word is never sought because of a structural prejudice, such as an un-refreshed list, that is no one’s fault | Fricker, in her own words, in two papers read in full: the paper that introduced testimonial injustice (2003, LIT-1049, NOTE-860), and her retrospective chapter (2017, LIT-1048, NOTE-853). A speaker receives the wrong degree of credibility “owing to a certain sort of unintended prejudice on the hearer’s part”. Deliberate manipulation of credibility is “a closely related but distinct injustice”. With Anderson, she accepts a structural form: when an un-refreshed list means some people’s views are never sought, “(through no one’s fault, let us add)”, that is pre-emptive testimonial injustice. It does not say every credibility deficit, or every omission from a list, is an injustice: a prejudice must cause it. | Active |
| THEORY-328 | An agent manipulated so that he meets every leading compatibilist condition is not morally responsible in the basic-desert sense, no responsibility-relevant difference separates him from an ordinarily determined agent, and so causal determination by factors beyond the agent’s control best explains why neither is responsible | Pereboom’s four-case argument, as two surveys report it: Caruso’s SEP entry (LIT-1047, NOTE-862), which quotes Case 2, and De Marco and Cyr (LIT-1045, NOTE-856), which quote Case 1 and state the best-explanation conclusion. Pereboom’s book (LIT-1006) is a source for the thesis it states in its Introduction and Chapter 1, not for the cases, which are in the unread Chapter 4. It does not say that determinism is true, or that manipulation itself is what defeats responsibility. The argument says it is the determination by outside factors, and that the manipulator is irrelevant. | Proposed |
| THEORY-329 v2 | In 32,479 Weibo posts of 2011–2016 scored with an emotion lexicon, posts tagged fake by the platform’s fact-checkers carry more anger and less joy than true posts from verified accounts, and a post’s share of anger words goes with more retweets after controls; whether the gap is due to falsity, and whether anger causes the spread, is not shown | Chuai & Zhao (2020), LIT-379, read in NOTE-852. In 32,479 Weibo posts from 2011–2016, lexicon-scored anger share is higher and joy share lower in fake than in true news, and in highly than in lowly retweeted news, under three scoring methods. With content, author and topic controls, anger share predicts more retweets within 48 hours and joy share fewer (R² 0.08–0.13). The paper calls this causal; the design is observational, and the fake set is selected for having spread. Active as a report of the association (ADR-065); the paper’s causal thesis is THEORY-1221, Proposed. | Active |
| THEORY-330 | After a forced phase in which each person experienced every memory load from three to nine items, the load that had given that person the best reward rate predicted their later choices better than one item fewer or one more, in a copying task where items are seen once and cannot be looked up again; a steeper reward for long lists raised chosen load, a higher price for errors did not, and about one person in five kept choosing a non-optimal load | Howes, Duggan, Kalidindi, Tseng and Lewis (2016), LIT-1062, read in NOTE-882. Participants copied names shown one at a time from a mock email to a calendar. Each person’s best list length in their own data predicted 55% and 46% of their choices, against 8–17% for the neighbouring lengths (N = 40 and 20). An exponential points schedule raised chosen length (6.99 against 5.07); forfeiting the whole trial on one error did not (5.00 against 5.05). 13 of 60 persistently chose a non-optimal length. There is no look-up and no model: the prediction is each person’s empirical argmax. Lieder and Griffiths’ description of it as a memorize-or-look-up trade (LIT-1071) does not fit the task. | Proposed |
| THEORY-331 | Counting the inference a model will serve as well as its training, the least-compute way to reach a fixed quality shifts toward up-front compute as expected inference volume grows: a smaller model trained on more data in Sardana et al., a larger pretrained model over test-time search in Snell et al.; test-time compute won only at low volume and on questions the small model already sometimes solved | Sardana et al. (2024; arXiv 2023), LIT-1070, read in NOTE-881, and Snell et al. (2024), LIT-1063, read in NOTE-869. Sardana et al. minimise training plus lifetime inference FLOPs at a fixed loss under a Chinchilla-fitted law: the optimum moves to smaller models trained longer as known demand grows (28% fewer FLOPs at 30B quality and 10^13 inference tokens), and 47 runs show loss still falling at extreme ratios but more slowly than the law predicts. Snell et al. match FLOPs between a small model with test-time search or revision and a ~14× larger model on MATH: test-time compute wins at a low ratio of inference to pretraining tokens on easier questions and loses at a high ratio, and on the hardest at every ratio. Both take expected use as a known aggregate; neither has staleness or uncertainty about demand, and Snell’s evidence is one model family on 500 questions. | Proposed |
| THEORY-332 v2 | For one index with no space limit, Bruno and Chaudhuri’s online tuner, which builds the index once the savings it would have given have risen by its build cost above their last low and drops it once they have fallen by the build cost below their last high, is not three-competitive: when every statement’s saving or loss is at most a fraction f of the build cost, a repeated workload makes it cost nearly 3 + 2f times the offline optimum, and one statement whose saving exceeds the build cost makes the ratio unbounded; no upper bound is shown | Bruno and Chaudhuri (2007), LIT-1095, read in NOTE-896. An always-on index tuner keeps, per index, the running sum of what each statement would have saved (updates counting as losses) and creates or drops the index when that sum moves by the build cost from its last extreme. The paper calls the single-index rule three-competitive, but its proof is one workload on which the ratio approaches 3, a lower bound. The reading’s own check found ratios up to 4.7 when one statement’s saving is near the build cost, and an unbounded ratio when it exceeds it; with every saving at most a tenth of the build cost no random workload passed 2.4, but a constructed one with steps at most fB approaches 3 + 2f (note of 2026-10-20). The multi-index tuner with a space limit is heuristic, and all costs are optimizer estimates. | Active |
| THEORY-333 v2 | Database cracking, which partitions a copy of a column in place as a side effect of each range query, measured in memory on 10^7 integers under uniformly random ranges, costs about 40% more than a scan on the first query and far less than sorting, gets cheaper per query with use, and stays cumulatively cheaper than sort-then-search until about 10^5 queries; that only the queried ranges get organized is not tested | Idreos, Kersten and Manegold (2007), LIT-1090, read in NOTE-892. Each range select splits, in place, the pieces of a column copy that hold its bounds and records the boundaries in an AVL tree, so later queries touch only edge pieces. In MonetDB on 10^7 values the first such select took 0.38 s against 0.27 s for a scan and about 3.3 s for sort-then-search, later selects 10 to 100 microseconds, and sorting overtook cracking in total only after about 10^5 queries. Every workload is uniformly random, so the paper’s claim that only ranges of interest get organized is asserted from the mechanism, not measured; there is no cost model and no rule for when a reorganization pays. | Active |
| THEORY-334 v2 | In copying a pattern of coloured blocks that stays in view, seven subjects told to work quickly looked back at the model about 1.3 times per block, and their commonest cycle, which looks at the model both before picking up a block and before dropping it, was the slowest per block in the authors’ observed tallies (about 3 s, against 1.5 s for a cycle that copies from memory); looks fell to 1.0 per block with model and copy 70° apart and to 0.7 with one-colour patterns that could be chunked, and in three subjects a colour change made during a saccade raised fixation time by about 129 ms after pickup against about 50 ms before; no statistics are reported | Ballard, Hayhoe, Pook and Rao (1997), LIT-1075, read in NOTE-883. Fixations are modelled as pointers that bind a program’s variable to a place in the world, so that only the task-relevant feature is fetched, just before use. In block copying, look-model, pick-up, look-model, drop was the commonest cycle (about 43% of cycles), at about 3 s a block against 1.5 s from memory; 70° separation cut looks from 1.3 to 1.0 per block, and one-colour patterns to 0.7. A colour changed mid-saccade mostly went unnoticed and cost time only once colour was held. The “carrying cost” of working memory is inferred from choice, not measured, and what is left in the world is raw input, not a computed result. Promoted 2026-10-20 on the observations alone (ADR-047 v3). | Active |
| THEORY-335 v2 | Selective accessibility, the account that comparing a target with a plausible anchor makes anchor-consistent knowledge more accessible and that this knowledge carries anchoring, fits the moderations of the effect by applicability, representativeness and plausibility that Strack and Mussweiler found, but its accessibility step is inferred, not measured: Harris et al.’s repetition of the recognition test of it, four times by lexical decision and once by continuous identification, found nothing in five preregistered experiments, with tasks that also missed direct picture priming | Strack & Mussweiler (1997), LIT-1064, read in NOTE-877, proposed the account and showed, in three small studies, that with the anchor number fixed the effect depends on whether the knowledge used to compare applies to the later estimate, and that plausible anchors slow the comparison and speed the estimate. Accessibility is inferred, never measured. Harris et al. (2019), LIT-1067, read in NOTE-876, repeated the recognition test (lexical decision, once continuous identification) of the accessibility step (Mussweiler & Strack 2000a, not held) five times at N = 128: anchoring was large and recognition of anchor-consistent words never moved (BF01 ≈ 21), but the same tasks missed direct picture priming. So the direct evidence is removed, not reversed; the account is neither refuted nor shown. Mussweiler & Strack 1999 (LIT-1078) is Unavailable. | Active |
| THEORY-336 v2 | An ideal observer is optimal relative to the information it is given, so a constrained ideal is the optimal decoder of a degraded input, not a restricted decoder of the full one; comparing real observers with ideals taken at successive stages of the visual system places losses by stage, and in early-vision tasks human performance is reported often to parallel the retinal-stage ideal across conditions while falling well below it | Geisler (2011), LIT-1055, read in NOTE-870. A review that defines the ideal observer as optimal “given the available information and any specified constraints”, and writes it as an expected-utility argmax over the posterior given the stimulus S or a constrained representation Z = g(S;θ). Constraints are added one at a time (optics, receptor sampling and noise, ganglion-cell summation), and human performance that parallels the retinal-stage ideal while falling below it is read as loss in central factors. The empirical parts are the review’s account of studies the record has not read. The review gives no formula for efficiency and no notion of an optimum over a restricted class of computations. | Active |
| THEORY-337 | In the comparative-question paradigm, judging whether a quantity is higher or lower than a high or low anchor pulls the later estimate of it toward the anchor, with large effects in five preregistered experiments of 128 people each, lasting through dozens of intervening word-recognition trials | Harris et al. (2019), LIT-1067, read in NOTE-876, and Strack & Mussweiler (1997), LIT-1064, read in NOTE-877. In five preregistered experiments (N = 128 each) on temperatures and car prices, estimates after a high anchor exceeded those after a low one every time (d ≈ 0.85–1.39), with 40 to 70 word-recognition trials between the comparison and the estimate. Strack and Mussweiler’s three small studies show the same effect, and that it can shrink or reverse when the knowledge used to compare does not apply to the estimate. This is the effect, not its mechanism: why the estimate moves is THEORY-335’s question and is not settled. | Active |
| THEORY-338 | For a list searched from the front, where reaching the i-th item costs i, moving each found item to the front costs at most twice what any rule costs on the same sequence, including rules that know the future (four times counting its own moves), a fixed order by access frequency is within no constant factor, and paying to rearrange ahead of need never helps; for paging, no online rule beats the offline optimum by less than n/(n − n_MIN + 1), and LRU meets that bound | Sleator and Tarjan (1985), LIT-1093, read in NOTE-903. With no probabilistic assumption, move-to-front on a sequentially scanned list is within 2 of the best algorithm in its class on every sequence, the rival being free to rearrange as it goes and to know the whole future; a list sorted once by frequency, transpose and frequency count are not within any constant; and any algorithm can be replaced by one no more expensive that makes no paid rearrangement (Theorem 3). For paging the online price of not knowing the future is n/(n − n_MIN + 1), the size of fast memory when the memories are equal. It is one list, or one two-level memory, with uniform items: it says nothing about bins, partitions or search that is not a scan. | Active |
| THEORY-339 | People’s answers to a probability query depend on their own answers to an earlier query whose result it can use: a person’s sub-answer predicts their later answer only when asked first, and a bias induced in a first judgment carries into a second only when the two share part of a hypothesis space, so reuse carries the earlier error with it; that reuse saves computation rests on one small response-time study and one secondary-task result | Dasgupta, Schulz, Goodman and Gershman (2018), LIT-1074, read in NOTE-875; Gershman and Goodman (2014), LIT-1056, read in NOTE-886; Dasgupta and Gershman (2021), LIT-1077, read in NOTE-865. In five small online experiments, an earlier answer shapes a later one only when the later query can use it, and errors in the first carry into the second. The authors call this amortized inference, reuse of past computation bought at a cost in bias. The speed benefit is shown once (median log-RT facilitation, n ≈ 50 per order) and otherwise assumed; storage and retrieval are free in the models; the 2021 review adds stale cached values from the planning literature, second-hand. No paper prices when reuse pays or touches stores outside the head. | Proposed |
| THEORY-340 | For answering membership in a static set of n keys with the fewest worst-case cell reads, sorted order with binary search is optimal only when the key universe exceeds a Ramsey-number threshold and table cells may hold nothing but stored keys or pointer symbols; it is beaten for small universes, and by two probes once one cell may hold an encoded value | Yao (1981), LIT-1097, read in NOTE-891. In the setting later called the cell-probe model, where only cells read are counted and both the arrangement and the adaptive search are arbitrary, ⌈lg(n+1)⌉ probes are needed by any scheme whose cells hold only keys of the set or a fixed stock of pointer symbols, once the universe is astronomically large (Theorems 1 and 1′). One probe suffices for m ≤ 2n − 2 (Theorem 2), and with one extra cell holding any value two probes suffice for m ≥ 2^{16n²} (Theorem 3). Building the table is free, so the paper prices lookup only and says nothing about whether sorting pays for itself. | Active |
| THEORY-341 | Inferring not-P from failure to prove P is a deduction only under two separate conditions: Clark shows that when every branch of the search for a proof of P ends in failure, not-P is a theorem of the completed database, and a search that does not finish licenses nothing; Reiter’s closed-world assumption, adding the negation of every ground atom the database does not entail, keeps a consistent Horn database consistent and can make a disjunctive one inconsistent | Clark (1978), LIT-1087, read in NOTE-894, and Reiter (1978), LIT-1088, read in NOTE-899 from his 1977 workshop report. Clark proves negation as failure sound with respect to the completed database (the clauses read as if-and-only-if definitions, plus axioms that distinct names denote distinct things), given a finite failure tree for some selection rule; it is incomplete in general. Reiter defines the closed-world assumption by entailment, reduces closed-world query evaluation to open-world atomic queries when the assumption is consistent, and shows it consistent for Horn and definite databases but not for Pa ∨ Pb. Soundness here is relative to the completion, not to the world, and neither paper says anything about a search cut short by time. | Active |
| THEORY-342 v2 | In AlphaZero on 9×9 Hex, at fixed playing strength, training compute and tree-search compute substitute along a straight line in log–log space, about 15× less search for each 10× more training over about two decades of training compute, down to a one-node search; the trade is measured for one search and counts no games played | Jones (2021), LIT-1069, read in NOTE-884. Across about 200 AlphaZero models on Hex boards 3×3 to 9×9, the best Elo for a given training compute follows one change-point curve, shifted by a fixed factor of compute per board row. On 9×9 only, iso-Elo contours of training against test-time search compute are straight in log–log space (fit: log test = −1.2·log train + 0.004·Elo + 29) over roughly 1e14–1e16 FLOPS-seconds of training, ending at a one-node search. One game, one nonstandard implementation, no uncertainty on the fitted coefficients, and no count of how many searches the trained agent will run, so it gives an exchange rate, not an amortization. | Active |
| THEORY-343 | In laboratory choice tasks, people offload cognition more as a task’s internal demand rises, but the choice follows their evaluation of the demand rather than its benefit: they offload where it gives no gain and more when less confident at equal ability, and offloading can lower memory for what was offloaded | Risko & Gilbert (2016), LIT-1059, read in NOTE-887. A review: in choice/no-choice studies of rotated displays, delayed intentions and short-term memory, spontaneous offloading rises with internal demand, but it also occurs where it gives no gain (writing items down about 40% of the time at a two-item load already at ceiling), rises with lower confidence after ability is controlled, and differs between displays of equal measured demand. Expecting to have a result stored externally went with poorer memory for it. The review reports no effect sizes, the cited studies were not read, and its metacognitive model is an unformalised box diagram; the drift toward external reliance is a prediction, not a finding. | Proposed |
| THEORY-344 v2 | An access method’s read, update and memory overheads, each a ratio to the base data alone with a floor of 1.0, are conjectured to trade so that bounding any two forces a lower bound on the third; the conjecture is unproved, its formal wording says no more than the floor already does, and the paper’s extreme designs show conflicts between pairs, read against memory and update against read, not a symmetric three-way trade | Athanassoulis et al. (2016), LIT-1085, read in NOTE-888. A six-page vision paper defines read, update and memory amplification and conjectures that an access method optimal on one cannot be optimal on both others. Its evidence is three one-paragraph propositions about extreme designs on an integer array, a qualitative triangle and a table of asymptotic I/O costs. The formal statement asserts only some lower bound on the third overhead, which every design has. The extremes are not symmetric: the memory-minimal design is also update-minimal. Build cost, workload and time are outside the triangle. | Active |
| THEORY-345 | Choosing indexes for a known mix of queries and updates, to minimize query cost plus a per-index upkeep, is NP-hard as the number of attributes and query types grows, and the tools built for it choose one stored order and a set of secondary indexes per table by searching configurations costed with the query optimizer’s own estimates, optimal at best relative to those estimates, with no proved guarantee for their heuristics and no term for the one-time cost of building | Piatetsky-Shapiro (1983), LIT-1089, read in NOTE-902; Finkelstein, Schkolnick and Tiberio (1988), LIT-1084, read in NOTE-898; Chaudhuri and Narasayya (1997), LIT-1083, read in NOTE-900. Minimum set cover reduces to choosing single-attribute secondary indexes under a known workload with a fixed upkeep per index. DBDSGN chooses the one clustered order and the secondary indexes per table against a frequency-weighted sum of access, update and upkeep costs plus storage, read from the System R optimizer; AutoAdmin picks at most k indexes by greedy search over what-if indexes. The model is steady state over a fixed workload: it prices upkeep against per-query savings, not a one-off build or sort against later lookups, and its optimality is relative to the optimizer’s estimates, never to measured execution. | Active |
| THEORY-346 | When information stays in view at a known place, people consult it less and rely on memory more as the time to reach it rises, in a graded trend across added delays from 0 to 3.2 seconds, even where the memory is weak and the display perfect; in one copying task a model that prices memory and display access in time alone, with no preference for either source, fits how many items people encode per look | Gray, Sims, Fu and Schoelles (2006), LIT-1073, read in NOTE-868, and Gray and Fu (2004), LIT-1058, read in NOTE-864. Adding a click to reach on-screen show information cut how often it was checked, and checks of finished settings came from memory. Lockouts of 0 to 3,200 ms on a Blocks World pattern cut looks and raised blocks placed per look, with linear trends. An ideal performer model with ACT-R memory equations and Q-learning on time alone fits four measures. That the control system has no bias toward the world is argued, not tested against a rival model. Errors in the 2004 study differed only against a group that memorized under several other changes, and the 2006 model has no wrong retrievals, no precomputation, no reuse across trials and no staleness. | Active |
| THEORY-347 | Belief bases with the same logical closure can revise to opposite conclusions on the same input, so a closed belief set does not fix its own revision; partial meet contraction of a base need not satisfy Recovery, and bases keep distinct inconsistent states apart, while a belief-set model reproduces the base difference only by attaching a different selection mechanism to the same set | Hansson’s Stanford Encyclopedia survey (2006, revised 2026), LIT-1072, read in NOTE-866, with Alchourrón, Gärdenfors and Makinson (1985), LIT-1050, read in NOTE-874. Bases {p, q} and {p, p ↔ q} have one closure, yet revised by ¬p one yields q and the other ¬q: statically but not dynamically equivalent. Base contraction escapes the Recovery that AGM proves for closed theories, and many inconsistent bases exist where there is one inconsistent closed set. A base marks which beliefs are held in their own right and recomputes the rest; it is not a record of reasons, sources or defeated alternatives, and the survey gives no result that bases handle iterated revision better. | Active |
| THEORY-348 | When staying in one state costs a fixed amount per request and leaving it costs a fixed one-time price, switching once the extra cost paid for staying equals that price is within 2 of the offline optimum on every request sequence, and no deterministic online rule does better; with a third option the best guaranteed ratio rises to 3 | Karlin, Manasse, Rudolph and Sleator (1988), LIT-1096, read in NOTE-893. A snoopy cache holding a shared block pays 1 per write to keep it current, or drops it and pays p to fetch it again on a later read. Dropping once the writes charged since the last read have cost p is strongly 2-competitive (Theorems 3.1 and 4.1); with a read- or write-through option the deterministic lower bound is 3 (Theorem 3.3). It is the first competitive analysis of a rent-or-buy decision, though the paper never uses the name, and its instance is when to stop maintaining a copy. Prices are fixed and known, the guarantee is worst case only, stale reads are forbidden rather than priced, and the authors call the practical significance “unclear”. | Active |
| THEORY-349 | For binary outcomes and a fixed representation of individuals, a predictor can pass every test in a bounded class without being close to nature: outcome indistinguishability to tests that see the sampled prediction is equivalent, with stated losses, to multicalibration over a closely related class of sets, a predictor meeting it exists at size polynomial in the tests’ size and the tolerance whatever nature’s complexity, and learning one is as hard as weak agnostic learning of the class | Dwork, Kim, Reingold, Rothblum and Yona (2021), LIT-1068, read in NOTE-885, and Hébert-Johnson, Kim, Reingold and Rothblum (2018), LIT-1052, read in NOTE-879. A predictor is outcome indistinguishable relative to a class of distinguishers when none can tell nature’s outcomes from outcomes drawn from the predictor, up to ε. With no access or sample access to the predictor this is equivalent to multi-accuracy or multicalibration over closely related classes, and a predictor meeting it exists at size O(s/ε²) (O(s/α⁴γ) for multicalibration), independent of nature. Learning a multicalibrated predictor is equivalent to weak agnostic learning of the class. Adequacy here is relative to the class, the outcome and the features, and is not unique; it is not closeness to the truth, and the papers say nothing about signal detection. | Active |
| THEORY-350 | Under a budget on maintenance time, a stored view’s upkeep depends on which other views are stored, so upkeep is not additive and adding a view can lower it, and greedily adding the single view of best saving per unit of upkeep can be arbitrarily bad; on OR view graphs a greedy over inverted tree sets gets 1 − 1/e of the saving of an optimum given as much upkeep, using up to twice the budget, if no tree-piece of the optimum alone exceeds the budget | Gupta and Mumick (1999), LIT-1092, read in NOTE-890, with the proofs of the journal version (2005), LIT-1080, read in NOTE-901, and the superadditivity first noted by Gupta (1997), LIT-1091, read in NOTE-889. Minimizing query cost subject to a cap on total maintenance time, one stored view can make another cheaper to keep current, so saving per unit of upkeep is not monotone and single-view greedy fails without bound (Example 2). Grouping views into inverted tree sets restores a 1 − 1/e guarantee, proved in 2005 (Theorem 8), for OR view graphs only, bicriteria, under an assumption on the optimum, with greedy stages exponential in general. The proof does not treat the negative effective costs the paper allows. Upkeep is a budget, not a cost traded against savings, and staleness and build cost are not modelled. | Active |
| THEORY-351 v2 | In a two-pilot airliner cockpit, setting the approach speeds as bugs on the airspeed indicators, prepared 25 to 30 minutes ahead in a low-workload phase from a card selected by the displayed gross weight, turns recall and scale reading at the moment of use into a judgement of spatial proximity, so the cockpit system remembers the speeds without either pilot’s memory being improved; this is argued by task analysis of mandated procedure, not measured | Hutchins (1995), LIT-1066, read in NOTE-867. A stylized task analysis of one airline’s MD-80 procedure, informed by observation but reporting no measurements. The speed-card booklet, filtered by the displayed gross weight, is the system’s long-term memory; the values pass through speech to bugs on two airspeed indicators, and on approach the pilots judge the needle’s nearness to a bug instead of recalling and reading speeds. The paper concludes that the memory is “not made primarily of pilot memory”. It analyses only success, for an anticipated, mandated and invariant task with a few values needed in a fixed order, so it says nothing about search for one item among many under a deadline. Cognition in the Wild (LIT-1060) is Unavailable. | Proposed |
| THEORY-352 | A pseudorandom generator exists if and only if a one-way function exists, where both are secure against uniform adversaries and every reduction is an oracle Turing machine, as statements about ensembles indexed by n; the construction from an arbitrary one-way function is only weak-preserving, so security at one length is bought at a much greater one | Håstad, Impagliazzo, Levin and Luby (1999), LIT-1051, read in NOTE-880, with Goldreich’s Foundations of Cryptography, LIT-1061, skimmed in NOTE-863 from the 1995 draft. Theorem 6.2.2: “There are one-way functions iff there are pseudorandom generators.” The hard direction runs one-way function → false entropy generator → pseudoentropy generator → generator, by uniform reductions, with seeds of length n^10 in the direct construction. Adversaries are algorithms; the paper has no circuit version, and that the proof carries over to non-uniform adversaries is the reading’s inference, not the paper’s statement. Everything is asymptotic. Goldreich states the theorem and does not prove it. | Active |
| THEORY-353 | For a logically closed theory, the contractions satisfying the six basic AGM postulates are exactly the partial meet contractions, and those satisfying the two supplementary postulates as well are exactly the ones whose selection of remainders is generated by a transitive relation; the theory alone does not fix the contraction, and the results concern one change of one fixed theory | Alchourrón, Gärdenfors and Makinson (1985), LIT-1050, read in NOTE-874, with Hansson’s survey, LIT-1072, read in NOTE-866. Contracting a closed theory A by x keeps what a selected set of maximal x-free subsets of A share; the six basic postulates characterize exactly these partial meet contractions (Observation 2.5), and with the two supplementary postulates exactly those selected by a transitive relation (Corollary 4.5). Revision follows by the Levi identity. A selection function or ordering must be added to A, and in the finite case distinct ones give distinct contractions. Nothing here concerns iterated change, where the selection comes from, or why a belief is held. | Active |
| THEORY-354 | An observer’s power to refute a predictor depends on its access to the predictor as well as on its budget: against tests that see only the sampled prediction a predictor of size O(s/ε²) always passes, but if fine-grained clique counting is hard, or BPP ≠ PSPACE, some cheap tests that may query the predictor adaptively pass only predictors about as costly as nature’s own | Dwork, Kim, Reingold, Rothblum and Yona (2021), LIT-1068, read in NOTE-885. Against sample-access distinguishers of size s an outcome-indistinguishable predictor of size O(s/ε²) always exists. Against oracle-access distinguishers, under fine-grained hardness of clique counting or BPP ≠ PSPACE, there are natures and polynomially many cheap distinguishers such that no predictor much cheaper than nature is indistinguishable. Non-adaptive queries add little; the power comes from adaptive queries. The results are conditional and asymptotic, with upper and lower bounds in different parameterisations; they say nothing about human observers or about which access a real auditor has. | Active |
| THEORY-355 | Agents arrange their surroundings so that perception and choice take the place of internal search, changing how much thinking a task needs without changing what can physically be done; the set-up is paid once and recovered over the later choice points the arrangement serves, so an arrangement whose scope is the whole task can repay a large set-up and a narrow one must repay within the next few actions, and the arrangement decays unless maintained; the savings are argued and piloted, not measured | Kirsh (1995), LIT-1076, read in NOTE-871, and Kirsh (1996), LIT-1057, read in NOTE-872. From video of cooks, assemblers and baggers and from informal observation, Kirsh classifies arrangements that simplify choice, perception and internal computation, frames their savings in search-complexity terms, and ties set-up cost to the number of choice points an arrangement serves. The 1996 paper adds a verbal investment rule with an interest factor for risk, one risk being that the change is not still present later, and upkeep against scatter. Neither paper gives a cost model or a measured saving; the 1995 paper says the savings do not “in general” admit meaningful quantitative estimation, and the 1996 paper puts mental cost outside its formalism. | Proposed |
| THEORY-356 | When stored views are never updated, greedily storing the view of largest marginal saving in query cost gets at least 1 − 1/e of the optimal saving on a data-cube lattice or any OR or AND view graph, against the optimum for the same number of views or for the space the greedy ends up using, which may exceed the budget by one view | Harinarayan, Rajaraman and Ullman (1996), LIT-1094, read in NOTE-895; Gupta (1997), LIT-1091, read in NOTE-889; Gupta and Mumick (2005), LIT-1080, read in NOTE-901. A stored answer is worth the saving on every query derivable from it, less what answers already stored save, and greedy on that marginal saving gets 1 − ((k−1)/k)^k ≥ 1 − 1/e of the best saving for k views; under a space budget the same holds against the optimum in the space the greedy actually uses (up to one view over), or 0.63 − f when no view takes more than a fraction f of the budget. The bound is on saving against storing the base view alone, not on query cost, and it holds only with no updates: once upkeep enters the objective it is proved only for AND graphs in which every view is queried more often than it is updated. | Active |
| THEORY-357 | Computational indistinguishability is strictly coarser than statistical closeness: without any assumption there are ensembles on at most 2^(n/2) strings that no circuit of size 2^(n/8) tells from uniform, though none of them is efficiently samplable, and an efficiently samplable pair of this kind exists if a pseudorandom generator does, since its output covers at most 2^n of the 2^l(n) strings; all of it is about ensembles indexed by n, not single pairs of distributions | Goldreich, Foundations of Cryptography vol. 1, LIT-1061, read in NOTE-863 (Skimmed, 1995 draft, Chapters 1–3 in full), with Håstad, Impagliazzo, Levin and Luby (1999), LIT-1051, read in NOTE-880. Proposition 3.3 proves by counting that some ensemble far from uniform fools every small circuit; its proof is non-constructive and the ensemble cannot be sampled efficiently. A generator’s output is efficiently samplable, indistinguishable from uniform by definition, and statistically far by an image count (§3.3.1). That a samplable such pair exists only if one-way functions do is cited to Goldreich 1990, not read. The book’s statistical difference has no factor ½, so it is twice total variation. | Active |
| THEORY-358 | In visual search among up to about 36 well-spaced items, a target that alone carries one colour or one distinctive shape part is found in time almost independent of the number of items, while a target identified only by a combination of features its neighbours carry separately takes time that grows linearly with the number of items, about twice as fast when the target is absent, the pattern of a serial self-terminating scan, and practice did not remove it; that conjunctions rather than similarity cause it is the paper’s reading, not its result | Treisman and Gelade (1980), LIT-1082, read in NOTE-897. With coloured letters on cards of 1 to 30 or 36 items, a blue letter or an S among brown Ts and green Xs was found at 3.8 and 2.5 ms per item, and a green T among the same distractors at 28.7 ms per item when present and 67.1 when absent, linear and in the ratio of a scan that stops at the first find; 13 sessions of practice did not change it. The paper reads the contrast as feature integration: conjunction structure, not similarity, makes search serial. That reading is contested by the similarity account of Duncan and Humphreys (LIT-1081), which the record could not obtain, and it does not follow that any item unique in one attribute pops out in a real pile. | Active |
| THEORY-359 | Cognitive mechanisms can be derived as the one, among those a brain can execute, that best trades the expected utility of its result against the opportunity cost of the time and resources it uses; the review shows the derivation reproducing many heuristics and biases, not that people are optimal, and the objective is per episode | Lieder & Griffiths (2020; online 2019), LIT-1071, read in NOTE-873. Resource rationality picks the heuristic that maximizes expected utility of its result minus the expected opportunity cost of the time and resources it uses (Eq. 3), averaged over environments consistent with what is known (Eq. 4), and a five-step method derives process models from it. The support is a review of others’ models recast in this frame, with numbers from those studies. The authors offer optimality as a methodological device, not a claim about people, and the method lets constraints be refitted to data. The objective is per episode, with no terms for storing, retrieving or reusing a result, or for its going stale. | Proposed |
| THEORY-360 v2 | In Kirsh and Maglio’s Tetris keystroke data, rotation began in earnest by 400 to 600 ms after a piece appeared, sometimes before it was fully in view, and at each of three skill levels drops preceded by a move to the wall and back were longer than ordinary drops, about 19 to 20 squares against 13 to 16 | Kirsh and Maglio (1994), LIT-1054, read in NOTE-878, with Kirsh (1995), LIT-1076, read in NOTE-871. In Tetris keystroke data, pieces are rotated more than plan-then-act would need, rotation starts by 400–600 ms, and a translate-to-wall check precedes longer drops. The authors define an epistemic action as one whose primary function is to cut the space, time or unreliability of the agent’s own computation, and argue these moves are of that kind. The saving is argued from a three-player pilot comparing physical with mental rotation, not measured in performance. The trade is offloading at the moment of use, once, with nothing stored; the paper sets itself against caching. Promoted 2026-10-20 on the timing and Table 1 alone (ADR-047 v3); the epistemic-action reading is held as THEORY-823. | Active |
| THEORY-361 | When every object but one has full grade in exactly one of two attribute-sorted lists and the one has full grade in both, finding it under min takes at least about half the objects’ worth of accesses for any algorithm that only reads the lists from the top and looks up objects already seen, and, with the tied objects in random order, about as many in expectation even for algorithms that may look up any object; a query on one attribute alone costs k accesses whatever the number of objects | Fagin, Lotem and Naor (2001; full version read as arXiv cs/0204046v1), LIT-1115, read in NOTE-924: Example 6.3 and Theorem 6.4, the paper’s proof that no algorithm is instance optimal once lucky lookups are allowed. With 2n + 1 objects, n + 1 high in each list and only one high in both, an algorithm that cannot guess must read at least n + 1 entries before it sees the target, and on a randomized family any deterministic algorithm needs at least n + 1 accesses in expectation. The paper uses the case to bound instance optimality. That it explains linear conjunction-search slopes in human vision is the record’s analogy, not the paper’s claim. | Active |
| THEORY-362 v2 | For nonrecursive Datalog or SQL views with safe stratified negation and stratified aggregation, under set or duplicate semantics, storing with each derived tuple only the number of its derivations suffices to maintain the view under insertions and deletions of base tuples: signed counts propagated through delta rules stratum by stratum give each tuple’s change as its new count minus its old, a tuple leaves when its count reaches zero, and a MIN or MAX group whose extreme is deleted is recomputed from the stored lower stratum | Gupta, Mumick and Subrahmanian (1993), LIT-1114, read in NOTE-915. Algorithm 4.1 evaluates delta rules in order of rule stratum and combines signed counts; Theorem 4.1 states it derives count(t^ν) − count(t) for every tuple, and Theorems 6.1 and 6.2 extend this to negated and aggregate subgoals. Its cost is argued to be close to evaluating the view and is not measured. All three theorems are stated without proof in this extended abstract. It does not say that a count suffices when support is cyclic: the paper keeps counting to nonrecursive views. | Active |
| THEORY-363 | For finding the top k objects under a monotone combining function from m lists each sorted by one attribute, with sorted and random accesses the only costs, the threshold algorithm is correct and on every database costs at most a constant times what any correct algorithm that makes no wild guesses costs; the constant is m + m(m−1)c_R/c_S, no deterministic algorithm does better when the function is strict, and once wild guesses are allowed no algorithm has such a guarantee on databases with ties | Fagin, Lotem and Naor (2001; full version read as arXiv cs/0204046v1), LIT-1115, read in NOTE-924. The threshold algorithm reads m attribute-sorted lists in parallel, looks up each new object’s other grades, and stops when k seen objects score at least the combined score of the last grades read. For every monotone combining function it is instance optimal among correct algorithms that make no wild guesses (Theorem 6.1), with ratio m + m(m−1)c_R/c_S, tight for strict functions (Corollary 6.2, Theorem 9.1). It is a guarantee relative to a class of algorithms under an access-cost model. It does not say that top-k queries are cheap: the absolute cost depends on the data, and is linear in N for some conjunctive queries. | Active |
| THEORY-364 | When each cached value is an interval its source guarantees to contain the current value, and a query must return an answer interval no wider than R whatever the true values, choosing the cheapest set of exact reads for a SUM is a 0/1 knapsack problem, NP-complete in general and solved by taking the narrowest intervals first when read costs are equal, and for a COUNT with a selection predicate the cheapest choice is the ⌈|T?| − R⌉ cheapest undecided tuples | Olston and Widom (2000), LIT-1117, read in NOTE-922. In TRAPP a cache holds intervals that sources keep valid by pushing a refresh whenever a value escapes, and each query names a width R its answer may have. The SUM answer is the sum of the intervals, so meeting R at least read cost is knapsack (profit = read cost, weight = width, capacity = R); COUNT under a predicate has a greedy optimum. Staleness becomes bounded imprecision, never error, and only the query-time cost of buying it down is optimized: the sources’ upkeep, the choice of interval widths and any cost of imprecision are outside the model. The MIN rule’s optimality proof is in an unread technical report. | Active |
| THEORY-365 v3 | In one study of a stack of proximity graphs on nested random subsets of the data, each element’s top layer drawn geometrically, greedy search on uniform random data in 8 dimensions needed a number of distance computations that grew no worse than logarithmically with the number of items and stayed below a single-layer navigable graph’s at every size tested, and in 4 dimensions the beam width needed for a fixed recall saturated; the logarithmic bound is derived only for exact Delaunay graphs of bounded degree, which the index does not build, and on 200 million SIFT vectors the measured growth departs from it | Malkov and Yashunin (2020), LIT-1098, read in NOTE-916 from arXiv v4. They build an index like a skip list, with proximity graphs in place of linked lists, and argue that search costs a constant per layer over O(log N) layers. That holds if each layer is an exact Delaunay graph of bounded mean degree. HNSW does not build such graphs, and Delaunay degree grows exponentially with dimension. For the graphs it does build, cost no worse than logarithmic is measured on uniform random data at d = 8, a saturating beam width at d = 4, and at d = 128 (200M SIFT) the growth departs from a logarithm. A proof for the graphs HNSW builds is QUESTION-187. The paper gives no worst-case bound and no recall guarantee. Construction is argued to cost about N searches. | Active |
| THEORY-366 | With a fixed number of data points and a query drawn independently of them, if the variance of the p-th power of the query-to-point distance divided by its mean tends to zero, the farthest point comes within any factor 1 + ε of the nearest with probability tending to one; independent coordinates meet this condition, while data on a low-dimensional subspace, or queries that fall inside well-separated clusters, escape it | Beyer, Goldstein, Ramakrishnan and Shaft (1999), LIT-1099, read in NOTE-917 from the authors’ 1998 technical report. Theorem 1: for n fixed data points and an independent query, var(d^p / E[d^p]) → 0 implies P[DMAX ≤ (1+ε)DMIN] → 1 for every ε > 0. The index m is arbitrary, so dimension enters only through the workload’s distance distributions. IID coordinates and several correlated or non-identical workloads satisfy the condition; a diagonal line, two latent degrees of freedom and queries inside clusters do not. The condition is sufficient, not necessary. The result concerns the ratio of distances at fixed n, and does not show that real high-dimensional data loses contrast, or that indexes fail. | Active |
| THEORY-367 v2 | For SPJU relational queries, which Buneman, Khanna and Tan’s tree model encodes, the minimal witnesses of an output tuple, the inclusion-minimal sets of source facts from which the query still derives it, are the minimal sets matched by single derivations and so are the same for every equivalent query, while where-provenance, the source location a value was copied from, can differ between equivalent queries | Buneman, Khanna and Tan (2001), LIT-1104, read in NOTE-920. Two meanings of the provenance of output data: why it is there (the witness basis, the source structures matched by each valuation that produces it) and where a value came from (the source paths bound to the output variable). The first is preserved by the paper’s rewrite system and, cut down to minimal witnesses, agrees across equivalent queries with equality conditions; the second is shown by example to depend on how the query is written. Proofs are omitted. It is not a theory of revision: additions to the source, negation, aggregation and strengths of support are all outside it. | Active |
| THEORY-368 v2 | On two-dimensional point sets constructed for the purpose, the authors’ code for fast-preprocessing DiskANN, HNSW and NSG, at parameters from the original papers, in most cases found none or few of a query’s five nearest neighbours until the search queue held about 10% of the points, for n from 10⁵ to 2·10⁶, and at that queue length ten graph indexes averaged recall@5 between 0.0 and 0.42; this is shown by experiment on one query per instance, and no theorem bounds these algorithms | Indyk and Xu (2023), LIT-1112, read in NOTE-910. The instances are grids of points in the plane in which a large cluster, reached first from the start vertex, lies closer to the query than the only points linked to its nearest neighbour. At queue length 0.1n, average recall@5 ranged from 0.0 (DiskANN) to 0.42 (KGraph). The paper calls the query time linear and says so “empirically”; the only argument beyond the experiment is an informal Ω(n/R) for DiskANN’s fast build. It does not show that these indexes fail on natural data or natural queries. | Active |
| THEORY-369 v2 | Under uniformly distributed, independent data and queries in the unit cube with Euclidean distance and a fixed number of points, an optimal nearest-neighbour search over any index that partitions points into blocks or convex clusters of at least two points must read a fraction of blocks that grows toward all of them as dimension rises; with a five-fold sequential advantage for scanning, estimates put the crossover at about 15–26 dimensions for rectangular and spherical bounding regions, and two tree indexes measured on 50,000 points lost to a scan beyond about 10 | Weber, Schek and Blott (1998), LIT-1107, read in NOTE-919. Under uniformity and independence, with the expected nearest-neighbour distance used as every query’s radius and integrals evaluated by Monte Carlo, the fraction of blocks read passes the 20% line at about d = 15–20 for rectangular regions and 26 for spherical ones. A crude bound for any convex clustering puts it below 610. The often-quoted “around 10” is the measured crossover for an R*-tree and an X-tree. The VA-file, a scan of compact per-vector approximations, is the paper’s alternative. Nothing is shown for data of low intrinsic dimension, and the finite-dimensional bounds are not rigorous as stated. The asymptotic statement, at fixed N and for clusters of two or more points, is proved by the record by a concentration argument. | Active |
| THEORY-370 | On an n × n lattice whose nodes also get long-range links drawn with probability proportional to lattice distance to the power −r, a searcher that knows only the target’s position and the links of nodes already reached delivers in expected time polylogarithmic in n only at r = 2: greedy routing then takes O((log n)²) steps, while for 0 ≤ r < 2 every such searcher needs Ω(n^((2−r)/3)) steps and for r > 2 Ω(n^((r−2)/(r−1))), even at r = 0 where short paths exist | Kleinberg (2000), LIT-1103, read in NOTE-923. Proved for the two-dimensional lattice: with nodes, local links and the number of long-range links fixed, changing only the exponent r of the long-range link distribution moves the expected delivery time of the best decentralized searcher from O((log n)²) at r = 2 to a power of n at every other r, including r = 0, where paths of polylogarithmic length exist. The upper bound is proved only for one local and one long-range link per node; the k-dimensional statement (r = k) is asserted, not proved; the family is inverse power laws of a distance every node can compute, so it does not show that no other link structure is navigable. | Active |
| THEORY-371 | For conjunctive queries without equality or comparisons, two queries are equivalent exactly when homomorphisms run both ways between the queries read as small databases, every such query has a minimal equivalent query unique up to isomorphism obtained by deleting atoms, and evaluating one against a database is NP-complete when the query is part of the input | Chandra and Merlin (1977), LIT-1111, read in NOTE-907. Reading a conjunctive query as its natural model, equivalence becomes a pair of homomorphisms (Lemma 13), the minimal equivalent query is unique up to isomorphism (Theorem 12), and evaluation with the query as input is NP-complete (Theorem 7), as is deciding whether one query is a folding of another (Theorem 11). The paper states equivalence, not containment, and does not state that containment or equivalence is NP-complete; those are corollaries later work attributes to it. Nothing here reaches queries with equality, comparisons, negation or union. | Active |
| THEORY-372 | For c-approximate near-neighbour search over n points in Euclidean space, space n^{1+ρu+o(1)} and query time n^{ρq+o(1)} are achievable on any data set whenever c²√ρq + (c²−1)√ρu ≥ √(2c²−1) (c√ρq + (c−1)√ρu ≥ √(2c−1) in Hamming space), and no list-of-points structure, the model of known data-independent hashing, does better on random instances; without that model the curve is matched only at query time n^{o(1)} by one or two cell probes | Andoni, Laarhoven, Razenshteyn and Waingarten (2017), LIT-1120, read in NOTE-918 from the arXiv full version. A data-dependent tree of spherical caps, with different thresholds for filing points and for routing queries, realizes every pair of exponents on the curve, for worst-case data, with constant success probability; the equal-threshold point is LSH. On random instances with d = ω(log n), list-of-points structures cannot beat the curve (a lower bound the paper calls conditional), and one- or two-probe cell-probe structures need n^{(c/(c−1))²−o(1)} words, the curve’s space at ρq = 0. Optimality for data-dependent schemes, for more probes, and for d = Θ(log n) is not shown. The curve prices space against per-query time for one query at a time; it has no workload and no build cost beyond space. | Active |
| THEORY-373 | For positive relational algebra on relations whose tuples are annotated from a commutative semiring, every query’s annotated answer equals its answer over provenance polynomials N[X] in the input tuple ids, evaluated at the input annotations, so set, bag, c-table and event-table semantics all factor through the polynomials; revaluing inputs can remove output tuples but never add them, and nothing is shown for negation, difference or aggregation | Green, Karvounarakis and Tannen (2007), LIT-1110, read in NOTE-913. Union and projection add tags, join multiplies them; the usual RA identities hold exactly when the tags form a commutative semiring, and a map of tags commutes with every query exactly when it is a semiring homomorphism. The polynomials N[X] are the free commutative semiring, so the annotated answer in any semiring is the polynomial answer evaluated at the input annotations (Theorem 4.3). It is a sufficiency result for revisions that re-annotate existing inputs, not a minimality result, and it excludes added facts and every nonmonotone operation. | Active |
| THEORY-374 v2 | Given views with conjunctive definitions, deciding that they answer a conjunctive query exactly is NP-complete in the size of the query and definitions, while a maximally-contained rewriting can be built in time polynomial in that size without saying whether it is exact; and finding all certain answers from the stored contents is polynomial in their size under the open-world assumption when the views are conjunctive and the query conjunctive or datalog, but co-NP-hard in that size under the closed-world assumption even for conjunctive views and queries | Halevy (2001), LIT-1116, read in NOTE-921, reporting Levy et al. 1995 (LIT-1100, read), Duschka, Genesereth and Levy, and Abiteboul and Duschka 1998 (not read). Reuse of stored views is graded: certifying an exact rewriting is NP-complete in the size of the definitions, building everything the views give (maximally contained) is polynomial, and the certain answers can cost a co-NP-hard search in the size of the stored data. Promoted 2026-10-21 on a re-derivation of the last two parts (ADR-047 v2); the primary papers they come from are unread. None of it prices recognition for definitions outside conjunctive queries and datalog, or says how costly recognition is on typical queries. | Active |
| THEORY-375 v2 | In one simulator evicting whole query-shaped cache regions, no replacement value function was best on every workload: a value based on distance from the current query beat LRU where queries clustered around a hot region or wandered with loops, while MRU was best on regular cyclic paths, by up to 2.3 times over the distance value and 9.6 times over LRU; none of the functions weighs what a region would cost to fetch again, and nothing is proved | Dar, Franklin, Jónsson, Srivastava and Tan (1996), LIT-1113, read in NOTE-904. With semantic regions as the unit of eviction, Manhattan distance from the most recent query beat LRU at every query size on a skewed selection workload, and a directional variant was best or tied on random map paths (LRU within 1.06) and on lollipop paths circling a square five or more times; MRU won on a single circuit and on plain squares (Manhattan 2.29 and LRU 9.57 on the 32 × 32 square). The study is simulation only, with synthetic paths and no refetch cost in any value; it shows that the best forecast of reuse depends on the workload, not that semantic distance is a robust rule. | Active |
| THEORY-376 v2 | In a simulated single-client, read-only database answering selection queries on one relation, describing cached data by the predicates of past queries let each query be answered partly from cache, with only the remainder Q ∧ ¬V sent to the server; this matched page caching on a clustered index, beat it on an unclustered one, and, on an unindexed attribute with a disk cache, answered over 60% of 1% queries without contacting the server; the cost of computing probe and remainder queries was not charged | Dar, Franklin, Jónsson, Srivastava and Tan (1996), LIT-1113, read in NOTE-904. In one simulator (one client, one server, a 10,000-tuple relation, 90% of queries in a hot 10%), semantic caching performed about like page caching on a clustered index, far better on an unclustered one, and on an unindexed attribute answered over 60% of 1% queries with no server scan. Space overhead depended on coalescing: 55 regions and about 275 factors for 1% queries without it. The result is measured, not proved; updates, joins and the CPU cost of reasoning about the cache’s contents were left out, so it does not show that predicate-described storage pays when finding the reusable part is costly. | Active |
| THEORY-377 v2 | In Olston, Loo and Widom’s simulations, a rule that multiplies a cached interval’s width by 1 + α on a pushed refresh with probability min{ρ, 1}, and divides it by 1 + α on a query’s exact fetch with probability min{1/ρ, 1}, settled within 1% of the best fixed width on one random walk and within 5% over eight walk settings; on a 50-host network-traffic trace, restricted to exact copies, it almost matched a tuned adaptive cache-or-not rule, and with a 50-value cache, where queries tolerated imprecision, it cost less; that it converges to the best width is argued, not proved | Olston, Loo and Widom (2001), LIT-1109, read in NOTE-912. The rule treats a pushed refresh as “too narrow” and a fetch as “too wide”, weighted by ρ = 2C_vr/C_qr, and needs no measurement of update rates, query rates or precision demands. Within 1% of the best fixed width on one random walk and within 5% over eight settings; with α = 1 and thresholds it tracked a 50-host traffic trace. With every copy forced exact it decided cache-or-not as well as an adaptive exact-caching rule, and did better where imprecision was allowed, except with a small cache. Convergence is argued from the balance condition only, all evidence is the authors’ simulation, and there is no worst-case guarantee. | Active |
| THEORY-378 | When items change as independent Poisson processes with known rates and a fixed total refresh rate is shared among them, refreshing every item equally keeps the copy at least as fresh and at most as old, averaged over time, as refreshing in proportion to change rate, for any spread of rates; the freshness-optimal share rises and then falls with change rate and gives nothing to items that change too fast for the budget | Cho and Garcia-Molina (2000), LIT-1119, read in NOTE-906. Freshness is the fraction of items equal to their source, age the mean time since an unseen change, both averaged over time and over equally weighted items. With fixed-interval refresh, uniform refresh is never worse than proportional on either measure, by convexity (proof in the authors’ technical report). Under a fixed budget the freshness-optimal allocation starves the fastest-changing items; the age-optimal one refreshes them somewhat more. It prices staleness as an objective under a fixed budget: there are no reads, no query savings, no build cost and no cost of a stale use, so it is a staleness term and not a model trading staleness against upkeep. | Active |
| THEORY-379 v2 | Fagin’s Algorithm finds the top k of N objects held in m attribute-sorted lists under any monotone combining function, and when the lists’ orderings are independent with at least m − 1 of them uniformly random it does so with O(N^((m−1)/m) k^(1/m)) sorted and random accesses with arbitrarily high probability; with dependent orderings the bound can fail | Fagin (1996/1999), LIT-1108, as reported by Fagin, Lotem and Naor (2001), LIT-1115, read in NOTE-924. Fagin’s own paper could not be obtained, and the reporting paper declines to describe the probability model (“off track”). It does correct one misreading: the only probabilistic assumption is independence of the lists’ orderings, not a uniform distribution of grades. For two lists the bound is √(Nk). It does not hold for anti-correlated attributes, where any algorithm can need about half the objects. | Active |
| THEORY-380 v2 | For datalog over a finite input instance annotated from a commutative ω-continuous semiring, with an answer’s tag defined as the sum over its derivation trees of the product of its leaves’ tags, the tags are the least fixed point of a finite polynomial system and factor through formal power series N∞⟦X⟧ in the input tuple ids; an answer tuple’s series has an infinite coefficient exactly when one of its derivation trees contains a tuple lying on a cycle of unit rules | Green, Karvounarakis and Tannen (2007), LIT-1110, read in NOTE-913. A recursive query can derive a tuple in infinitely many ways, so polynomials do not suffice and the semiring needs infinite sums. With ω-continuous semirings and the provenance semiring N∞⟦X⟧ the paper states the analogues of the relational results: a fixed-point characterization (Theorem 5.6), factorization (Theorem 6.4), and a test for infinite coefficients (Theorem 6.5), with algorithms that decide finiteness and compute coefficients. Proofs are not given. Plain N and N[X] are excluded, the provenance can be an infinite object held only as equations, and negation remains outside. | Active |
| THEORY-381 | In the cell-probe model, a near-neighbour structure on n random points that answers in t probes with m cells of w bits must satisfy m^t·w/n ≥ the robust expansion of the metric’s neighbourhood graph at measure 1/m^t (and (mwt/n)^t ≥ its vertex expansion if deterministic), so in expanding spaces such as the hypercube fast queries need space polynomially larger than the data; the bounds are average case, approximate, and fall off exponentially in t | Panigrahy, Talwar and Wieder (2010), LIT-1102, read in NOTE-914 from the arXiv preprint. For graphical neighbour search, to which decision approximate near neighbour reduces, on data drawn so that neighbourhoods rarely overlap: deterministic t-probe structures satisfy (mwt/n)^t ≥ Φv and m^t·t·w/n ≥ Φv(1/m^t); randomized ones satisfy m^t·w/n ≥ Φr(1/m^t, γ/t) and (mwt⁴/n)^{2t} ≥ Φr(1/m, γ/t). On the hypercube this gives space n^{1+Ω(1/(ct))} at approximation c and n^{Ω(1/(tε²))} at 1 + ε; a one-probe structure matches on Cayley graphs; low-contention dynamic structures need update time at least Φr(τ, 1/(4t²)) over poly(t). Tight only for constant t; nothing about worst-case or structured data, workloads or build time. | Active |
| THEORY-382 v2 | When a web server keeps each page fragment either cached and invalidated by updates or stored and refreshed after them, materializing trades staleness for response time, and in one synthetic simulation with fixed costs a periodic greedy that moves a capped number of fragments between the two, to keep the share of fresh fragments served above a set threshold, tracked that threshold by the authors’ reading of its curves, answered faster than caching alone and recovered from overload by materializing everything; no bound on its distance from the best plan is shown | Labrinidis and Roussopoulos (2003), LIT-1105, read in NOTE-911. Quality of Data is the share of fresh fragments in served pages; OVIS(θ) estimates per fragment the change in response time (hits and misses against refresh load) and in QoD from switching policy, and each period greedily switches up to MAX_CHANGE fragments to spend a QoD surplus on speed or buy back a deficit. The paper asserts the greedy step is best under the cap and proves nothing; the evidence is one simulator with uniform costs and no comparison with an optimum. The reading the evidence does not support: that this is a joint cost model of build, upkeep, staleness and savings. Staleness is a user-set threshold, not a price, and switching and storage are free. | Active |
| THEORY-383 v2 | On one Apache and Informix server answering cheap indexed selections over 1000 pages, a page whose query result was stored in the DBMS and refreshed on every update answered more slowly than one recomputed on each request at five or more updates per second, which the authors explain by reading the stored result costing about as much as recomputing it and its refresh loading the same DBMS, while a finished page stored at the web server and rewritten on every update answered 10 to 230 times faster than either | Labrinidis and Roussopoulos (2000), LIT-1118, read in NOTE-908. Three ways to serve a database-generated page under online updates, with no stale reads allowed: compute on request, store the query result in the DBMS, or store the finished page at the web server. A cost model sums access and update costs by frequency; the per-page selection problem is stated and not solved. On their testbed the page stored at the web server won at every load, and the result stored in the DBMS lost to recomputation at five or more updates per second. The reading the evidence does not support: that storing an answer pays whenever it is reused enough. Where it is stored decided the outcome, and the generalization to other systems is the authors’ expectation, not a measurement. | Active |
| THEORY-384 | A nearest-neighbour graph built by pruning each point’s links against all other points with a factor α > 1, so that from every point some link is α times closer to any other point, lets greedy search from any start reach a ((α+1)/(α−1) + ε)-approximate nearest neighbour in O(log_α(∆/((α−1)ε))) steps of cost O((4α)^d log ∆), for doubling dimension d and aspect ratio ∆; the ratio is tight and the dependence on ∆ cannot be replaced by one on n, and the build takes O(n³) time done naively | Indyk and Xu (2023), LIT-1112, read in NOTE-910. Proved for DiskANN’s “slow preprocessing” build, not the build DiskANN implements. The guarantee rests on one property of the graph (α-shortcut reachability, α > 1), gives a constant approximation, not exact search, is logarithmic in the aspect ratio ∆, which can exceed n by far, and has a per-step cost exponential in the doubling dimension. HNSW and NSG prune with α = 1 and are not covered. | Active |
| THEORY-385 v2 | In HNSW over 10-dimensional data in 100 isolated clusters, linking each new item to its nearest neighbours leaves part of the bottom layer unreachable from the entry point and caps recall well short of 1 however wide the query search, while linking a candidate only when it is nearer the new item than to any neighbour already kept keeps that layer connected and reaches recall near 1 with about half the links; on uniform data at 10 and 64 dimensions the two rules differ little; shown in Malkov and Yashunin’s own tests on 10 million points and in an independent re-run on 30,000, which found the nearest-neighbour rule capped at a recall@10 of 0.72 to 0.83 against 0.999, at matched build cost too | Malkov and Yashunin (2020), LIT-1098, read in NOTE-916. In HNSW, each new element’s neighbours are chosen either as its M nearest candidates or by a pruning rule that keeps a candidate only if it is nearer the new element than to any neighbour already kept, a rule related to the relative neighbourhood graph. On 10M random d = 10 vectors in 100 isolated clusters, nearest-neighbour links failed to reach high recall and the pruning rule did not. In every test reported, the rule was at least as good. Its gain was largest at low dimension, at high recall, and on clustered data, and small on uniform or very high-dimensional data. These are the authors’ benchmarks: one clustered dataset, synthetic, with no independent replication in this reading. Re-run independently at smaller scale on promotion (2026-10-20), with the same result. | Active |
| THEORY-386 | When a cached interval of width W is kept valid by its source, which pushes a refresh at cost C_vr whenever the value leaves it, and queries fetch the exact value at cost C_qr whenever it is too wide, and the chances of the two per step go as 1/W² and as W, the expected refresh cost is least at W* = (ρK₁/K₂)^(1/3) with ρ = 2C_vr/C_qr, where ρ times the chance of a pushed refresh equals the chance of a fetch | Olston, Loo and Widom (2001), LIT-1109, read in NOTE-912. The cost rate Ω(W) = C_vr·K₁/W² + C_qr·K₂·W is least where ρ·P_vr = P_qr. The minimum is calculus on assumed forms. P_qr ∝ W follows exactly from uniform precision demands; P_vr ∝ 1/W² comes from a Chebyshev bound on a random walk used as an estimate, and the paper’s simulation of a random walk measured both proportionalities. Staleness here is priced as refresh traffic: the source guarantees validity, so a stale read is imprecise but never wrong, and there is no build cost and no cost of a wrong or imprecise answer. | Active |
| THEORY-387 v2 | For positive recursive Datalog views under set semantics, deleting every derived tuple that has any derivation through a deleted base fact, then restoring each deleted tuple that still has a derivation from what remains, then adding what insertions derive, leaves exactly the tuples derivable from the new base (E − Δ⁻) ∪ Δ⁺, with no derivation counts stored; the extension to stratified negation and aggregation is asserted, not shown, and the size of the overestimate is not measured | Gupta, Mumick and Subrahmanian (1993), LIT-1114, read in NOTE-915. DRed runs stratum by stratum: semi-naive Δ⁻-rules compute an overestimate of deletions, δ⁺-rules put back those with a derivation in the reduced database, and Δ⁺-rules add insertions. Theorem 7.1 states the result contains t if and only if t has a derivation in (E − Δ⁻) ∪ Δ⁺; the proof is in a 1992 AT&T report the record has not seen. The paper asserts, and does not show, that DRed handles stratified negation, aggregation and rule changes, that it beats the PF algorithm by up to an order of magnitude, and that it is slower than counting on nonrecursive views. | Active |
| THEORY-388 | Locality-sensitive hashing answers approximate near-neighbour queries over n points with O(n^ρ) hash evaluations in O(dn + n^{1+ρ}) space, where ρ = ln(1/p1)/ln(1/p2) is set by how much more often near pairs collide than far ones and is at most 1/(1+ε) for approximation 1+ε in Hamming space, with constant success probability per query; the paper gives upper bounds only and proves no limit on what organizing can buy | Indyk and Motwani (1998), LIT-1106, read in NOTE-905 from the authors’ 1999 expanded version, compared with the STOC text. A hash family under which points within r1 collide with probability at least p1 and points beyond r2 with at most p2 gives n^ρ random tables, each storing every point: O(dn + n^{1+ρ}) space and O(n^ρ) hash evaluations per query, ρ = ln(1/p1)/ln(1/p2), for the decision version, which ring-cover trees connect to approximate nearest neighbour with polylog overhead. Bit sampling gives ρ ≤ 1/(1+ε) in Hamming space and, by embedding, ℓ_p for p in [1, 2]; the STOC text states 1/ε and only for ε > 1. Grid bucketing gives Õ(d) queries for n·O(1/ε)^d preprocessing. Preprocessing is counted as space. Nothing is proved about whether these exponents can be beaten. | Active |
| THEORY-389 | For conjunctive queries and views without comparison predicates, a stored view can be used in an equivalent rewriting of a query exactly when the view’s body maps homomorphically into the query’s, a minimal rewriting needs no more literals than the query, and deciding whether a rewriting shorter than the query or one using only the views exists is NP-complete in the size of the query and view definitions; with comparisons in both, deciding whether any rewriting uses the views is Π2p-complete | Levy, Mendelzon, Sagiv and Srivastava (1995), LIT-1100, read in NOTE-909. Every use of a view in an equivalent rewriting comes from a containment mapping from the view into the query (Proposition 3.1); without comparisons a locally minimal complete rewriting has at most as many literals as the query (Lemma 3.5), which puts the problems in NP, and they are NP-complete (Theorems 3.7, 3.9, 3.10), with two independent sources of hardness. The results are worst case, in the size of the definitions rather than the stored data, for equivalent rewritings under set semantics only; they do not say recognizing reuse is costly in practice, and they do not cover contained (partial) rewritings. | Active |
| THEORY-390 | Any distribution of n × N matrices whose norms concentrate as Johnson–Lindenstrauss proofs require gives the restricted isometry property of order k with probability at least 1 − 2e^{−c₂n} for k ≤ c₁n/log(N/k), by a union bound over (12/δ)^k net points on each of the (eN/k)^k sparse supports; this makes k log(N/k) measurements sufficient for Gaussian, ±1 and sparse three-valued matrices, and does not show they are necessary | Baraniuk, Davenport, DeVore and Wakin (2008), LIT-1156, read in NOTE-931 from the author-posted copy. The only assumption is the concentration inequality Pr(|‖Φx‖² − ‖x‖²| ≥ ε‖x‖²) ≤ 2e^{−nc₀(ε)}, met with Achlioptas’s c₀(ε) = ε²/4 − ε³/6. The proof is the JL argument run over a net on every sparse support, plus a step from the net to the whole subspace. Necessity of k log(N/k) is recalled from Gelfand widths, not derived from concentration, and constants are implicit. | Active |
| THEORY-391 v3 | Recovery of a k-sparse vector by ℓ₁ minimization from n random measurements in dimension N switches, as N grows with δ = n/N and ρ = k/n fixed, from near-certain success to near-certain failure across a curve ρ(δ) that, for Gaussian matrices, the authors’ earlier face-counting theorems fix; in 2,948,000 optimizations at N = 200, 400 and 1600, eight non-Gaussian ensembles approached that curve in a way consistent with gaps shrinking as N^(−1/2), an exponent fitted on the same data, while at finite N the location depended on the ensemble | Donoho and Tanner (2009), LIT-1160, read in NOTE-933 from arXiv 0906.2530v1. The Gaussian transition is a theorem of the authors’ earlier papers, restated here. The universality is an observation from 2,948,000 optimizations at N = 200, 400 and 1600: strict finite-N universality is rejected, and agreement as N → ∞ is not rejected. Sparse and Hadamard matrices sit about one transition width low at small N. The title states only what was measured. Whether the agreement is a limit theorem is QUESTION-168. | Active |
| THEORY-392 v2 | Every map from an n-point subset of a metric space into Hilbert space extends to the whole space with Lipschitz constant at most K√(log n) times its own, by dimension reduction to K log n coordinates followed by Kirszbraun and the non-linear Hahn–Banach theorem; for L_p, 1 ≤ p < 2, the constant must be at least δ(Log n/Log Log n)^(1/p−1/2), so √(log n) is right up to a log log factor in the worst case | Johnson and Lindenstrauss (1984), LIT-1153, read in NOTE-930. Theorem 1 proves Marcus and Pisier’s conjecture L(X, n) ≤ K(Log n)^(1/2) for every metric space X; Theorem 3 gives L(p, n) ≥ δ(Log n/Log Log n)^(1/p−1/2) for 1 ≤ p < 2, hence L(∞, n) ≥ δ(Log n/Log Log n)^(1/2). The √(log n) comes from the √k cost of passing between ℓ₂ᵏ and ℓ∞ᵏ, with k of order log n. Whether the upper bound is sharp the paper leaves open, and the constants are loose. | Active |
| THEORY-393 | Any two families of n vectors of norm at most 1 have images in ⌊C log(2 + ε²n)/ε²⌋ dimensions whose cross inner products ⟨x_i, y_j⟩ are each within an additive ε of the originals, found by a randomized polynomial-time algorithm, which for small ε is below the log n/ε² of the Johnson–Lindenstrauss lemma; only cross products are kept, the new vectors’ norms are not bounded, and whether one set can be embedded that small is open | Alon and Klartag (2017), LIT-1151, read in NOTE-929 from arXiv v4. Theorem 1.2 answers, in a bipartite form, Larsen and Nelson’s question whether log n can become log(2 + ε²n) in the JL lemma. The proof is convex geometry: Khatri–Šidák bounds the Gaussian measure of a body of slabs, and a weakened low M*-estimate puts a random t-dimensional subspace close to every scaled a_i. Conjecture 2.4, the same with norms O(1), is proved only for t of order n (Theorem 2.5). It is not an embedding of one point set and says nothing about distances. | Active |
| THEORY-394 | Every n-point metric space embeds in Euclidean space of O(log n) dimensions with distortion O(log n), by distances to random sets of every scale followed by Johnson–Lindenstrauss, and constant-degree expanders need distortion Ω(log n) in every ℓ_p with 1 ≤ p ≤ 2, of any dimension, so O(log n) is tight in the worst case; the constants are unspecified, the lower bound rests on Leighton and Rao’s flow–cut gap, and nothing is shown for trees or for p > 2 | Linial, London and Rabinovich (1995), LIT-1155, read in NOTE-928 from the authors’ February 1995 manuscript. Theorem 3.2(1) states Bourgain’s theorem (LIT-1161, unread): every n-point metric embeds in O(log n)-dimensional Euclidean space with distortion O(log n). The paper reproves the distortion with a randomized map into ℓ_p^{O(log² n)} built from distances to O(log n) random sets of each size 2ˡ, and gets the dimension from Johnson–Lindenstrauss. Proposition 4.2 shows that every embedding of a constant-degree expander into ℓ_p, 1 ≤ p ≤ 2, has distortion Ω(log n), from the expander’s Ω(log n) gap between flow and cut. Together these answer Johnson and Lindenstrauss’s Problem 4 in the negative, which the paper does not say. | Active |
| THEORY-395 v2 | For ε between about lg^0.5001 n/√min{n, d} and 1, some n-point set in ℝ^d needs Ω(ε⁻² lg(ε²n)) dimensions under any map, linear or not, that keeps its pairwise squared distances within 1 ± ε, so a random projection with a union bound is optimal up to a constant for the worst set; nearly orthogonal sets can need fewer, and the bound says nothing about typical data | Larsen and Nelson (2017), LIT-1154, read in NOTE-925 from arXiv v2. Theorem 2 removes the lg(1/ε) gap that Welch, Levenshtein and Alon left, for arbitrary maps. The proof is an encoding argument over a family of k-sparse vectors with k ≈ ε⁻², ending at nm = Ω(kn lg(d/k)). It is a worst-case bound by existence with an untracked constant. It is not a phase transition, and the paper notes that ε-incoherent sets fit in o(ε⁻² lg n) dimensions for small enough ε. | Active |
| THEORY-396 | Every Lipschitz map from an n-point metric space into any Banach space extends to any containing space with Lipschitz constant at most C log n/log log n times its own, by averaging over random partitions at every scale, and every n-point subset of L₂ extends into any Banach space at C√(log n) after Johnson–Lindenstrauss dimension reduction; for maps into Hilbert space this is no improvement on K√(log n), and whether √(log n) suffices for every target is left open | Lee and Naor (2005), LIT-1152, read in NOTE-927 from the authors’ January 2004 preprint. Theorem 1.10 (Theorem 5.1(4)): ae(X) ≤ C log n/log log n for every n-point metric space X, bounding the extension constant over every superspace and every Banach target at once, improving Johnson, Lindenstrauss and Schechtman’s C log n. Theorem 1.12: eₙ(L_p, Z) ≤ C(p)(log n)^{1/p} for 1 < p ≤ 2, C√(log n) at p = 2, through the Johnson–Lindenstrauss lemma and e(ℓ₂ᵈ, Z) ≤ C√d. For Hilbert targets Johnson and Lindenstrauss’s K√(log n) (THEORY-392) stays the better bound, and the paper states as open whether O(√(log n)) holds for every metric domain and normed target. | Active |
| THEORY-397 | A random linear map into k ≥ 4(ε²/2 − ε³/3)⁻¹ ln n dimensions keeps every pairwise squared distance of a fixed set of n points in ℓ₂ within 1 ± ε, because each difference vector’s squared length concentrates with tails exp(−(k/2)(ε²/2 − ε³/3)) and a union bound over the pairs costs only ln n; the proofs cover a random subspace, Gaussian entries and independent zero-mean ±1 or √3·{+1, 0, −1} entries, and no matrix with nonnegative entries | Dasgupta and Gupta (2003), LIT-1157, read in NOTE-932, give the explicit bound for a projection onto a random subspace; Johnson and Lindenstrauss (1984), LIT-1153, read in NOTE-930, prove the lemma with k = [K(τ) log n] and K ≥ (10/τ)² by Lévy’s isoperimetric inequality; Achlioptas, LIT-1159, read in NOTE-926 from a 2002 draft, carries the same k₀ to independent ±1 and sparse three-valued entries. The guarantee is for a fixed finite set, on squared distances, and it rests on entries being zero-mean. It says nothing about maps that go up in dimension or are followed by a threshold. | Active |
| THEORY-398 v2 | A Lipschitz map from a subset of a metric space whose points are at least ε apart and whose diameter is D extends to the whole space into Hilbert space with Lipschitz constant at most 6D/ε times its own, and, by Benyamini’s argument in the same paper, into any Banach space with at most 4D/ε, with no dependence on the number of points | Johnson and Lindenstrauss (1984), LIT-1153, read in NOTE-930. Theorem 2 gives 6D/ε for maps into ℓ₂, through ℓ₁ and a weak form of Grothendieck’s inequality; Benyamini’s appendix gives 4D/ε for any Banach target, through a retraction of ℓ∞(Γ) with Lipschitz constant at most 2. The bound trades the count of points for the spread of the set. Whether either constant is best possible is not discussed. | Active |
| THEORY-399 | Storing every inner product of n points of the unit ball of R^k to additive error ε takes Θ(n log n/ε²) bits once k ≥ log n/ε² and Θ(nk log(2 + log n/(ε²k))) below, for 1/n^0.49 ≤ ε ≤ 0.1, and comparing these counts across dimensions shows that some n such points cannot be mapped into fewer than Ω(min{k, log(2 + ε²n)/ε²}) dimensions with additive error ε for every ε ≥ 2/√n; this is a worst-case lower bound with unstated constants, the small-ε bit count is open for k above that dimension, and no one-family embedding that small is proved | Alon and Klartag (2017), LIT-1151, read in NOTE-929 from arXiv v4. Theorem 1.1 gives the bits of an additive ε-distance sketch for every k when 1/n^0.49 ≤ ε ≤ 0.1, by a volume argument above and a packing of net points against random probes below. Since an embedding is a sketch, Corollary 2.1 re-proves Larsen and Nelson’s bound in that range, and Corollary 2.3, using the Gaussian correlation inequality in place of a union bound, extends it to every ε ≥ 2/√n with log(2 + ε²n) in place of log n. The dimension statements are for additive error on squared distances of points of norm at most 1; the relative form for small ε follows but is not stated. The matching upper bound for one set is open. | Active |
| THEORY-400 | A metric space that admits, at every scale, random partitions into small pieces with each point padded away from piece boundaries with constant probability is absolutely Lipschitz extendable: maps from it into any Banach space extend to any containing space at O(1/padding), which gives C log λ for doubling constant λ, C r² for K_r-minor-free graph metrics, C(g+1) on genus-g surfaces and C√d from ℓ₂ᵈ; the bounds are upper bounds only, and the method needs a decomposition the domain may not have | Lee and Naor (2005), LIT-1152, read in NOTE-927 from the authors’ January 2004 preprint. Theorem 4.1 turns (ε, δ)-padded random partitions of the domain at every scale into a C/(εδ)-gentle partition of unity, and Lemma 2.1 turns that into extensions of constant 3C/(εδ) into any Banach space; Lemma 3.8 carries the partitions from X to any superspace. Theorem 5.1 gives ae(X) ≤ C log λ(X), ≤ C r² for K_r-minor-free graph metrics, ≤ C(g+1) on surfaces of genus g, and e(ℓ₂ᵈ, Z) ≤ C√d, generalizing Johnson, Lindenstrauss and Schechtman’s Cd and Matoušek’s trees. No lower bound shows any of them tight. | Active |
| THEORY-401 | A fair lottery on the natural numbers has a uniform, regular probability defined on every set of tickets, by normalised numerosity with values in the hyperrationals; it is fixed only up to a choice of free ultrafilter, it is hyperfinitely and not countably additive, and its standard part is ordinary asymptotic density | Wenmackers (2011), LIT-163, chapter 2, read in NOTE-139. P_num(A) = num(A)/α is defined on all of 𝒫(ℕ), gives each ticket 1/α > 0, and satisfies FAIR, ALL and a hypercountable form of SUM (eqs. 2.20–2.27). Proved, given the axiom of choice. It is not a free lunch: one solution per free ultrafilter, no invariance under relabelling, no countable additivity, and by the author’s own admission it is empirically indistinguishable from the finitely additive real-valued solution. | Active |
| THEORY-402 | Collective intelligence is resource-bounded computation with a larger but modular budget: a group has more sensing, state, processing and action than any member, and pays coordination and cooperation costs because those resources sit in autonomous members, so the same trade-off yields groups that do better than their members on some tasks, groups that run qualitatively different algorithms, and groups that do worse | Pilgrim et al. (2025), LIT-046, read in NOTE-055, with Dreyer et al. (2024), LIT-075 (NOTE-040), as its clearest instance. The paper offers a four-dimensional resource inventory, a catalogue of constraints and a mapping to mechanisms, and calls the known forms of collective intelligence “aspects of a single unifying principle”. NOTE-055 judges it a vocabulary, not a derivation: the resources have no metric, so the framework cannot say in advance when costs outweigh gains, and its “predictions” are research questions. Filed Proposed as the account the vocabulary states. | Proposed |
| THEORY-403 | The single-photon Mach–Zehnder phenomenology with balanced beamsplitters and phases 0 or π, including which-way detection, the bomb tester, delayed choice and the quantum eraser, is reproduced exactly by a local, deterministic classical field model with an epistemic restriction, so that slice of interference forces neither complementarity, nor observer-dependent reality, nor nonlocality | Catani, Leifer, Schmid & Spekkens (2021), LIT-019, read in full in NOTE-018. Each mode carries a binary occupation and a binary phase; an agent may know at most one of N, Φ, N⊕Φ; the beamsplitter swaps N_L with Φ_L⊕Φ_R. The model gives the quantum statistics for the phase shifter, which-way detection, the bomb tester (¼), delayed choice and the eraser. The existence proof holds for that fragment. The paper’s further claim, that the model is generalized-noncontextual and so classical by its preferred criterion, is asserted, not proved, and unbalanced beamsplitters already admit a no-go. | Active |
| THEORY-404 v2 | With a common prior, a sender who commits to a signal the receiver observes can induce any distribution of posteriors whose mean is the prior, so an openly designed experiment moves a fully informed Bayesian receiver whenever the concave closure of the sender’s value lies above its value at the prior; at the optimum, under the paper’s tie-breaking, the receiver is certain when she takes the sender’s worst action and indifferent when she takes another | Kamenica & Gentzkow (2011), LIT-1021, read in NOTE-717 with the proofs. Proved results (Proposition 1, Corollary 2, Propositions 4 and 5) for a single ideal Bayesian receiver, a finite state space, commitment and sender-preferred tie-breaking. A judge who knows the investigation was designed to convict convicts 60 percent of defendants when 70 percent are innocent. The paper does not analyse manipulation, does not compute the receiver’s welfare and does not cite Blackwell. | Active |
| THEORY-405 v2 | Adding one classifier-free guidance term per concept to a diffusion model’s unconditional noise prediction samples images that satisfy several concepts at once without retraining, and on synthetic scenes it composes object positions far better than compositional energy-based models but relations no better; the reading of the summed score as the score of a product of experts holds only for concepts conditionally independent given the image, unit weights, a conservative field and the noise-free distribution | Liu, Li, Du, Torralba & Tenenbaum (2022), LIT-770, read in NOTE-597. CLEVR object positions, 1/2/3 components: 86.42/59.20/31.36% against an EBM’s 70.54/28.22/7.34%. Relations: 60.40/21.84/2.80% against 78.14/24.16/4.26%. FFHQ attributes are comparable to LACE. Text-model composition (GLIDE, Stable Diffusion) is shown only in figures, with attribute confusion and hybrid objects among its listed failures. The product is derived at the data distribution and applied at every noise level, which NOTE-597 notes is in general not the score of the noised product. | Active |
| THEORY-406 v2 | Self-presentations that differ by audience coexist without trouble while the audiences are kept apart by spatial, social and temporal boundaries, and collide when a medium removes the boundaries; networked publics make the collision frequent and often unseen by the person it happens to | boyd (2008), LIT-1001, after Meyrowitz (1985), read in part: §1.5, §4.4, the Top Friends passage and every passage on context, segmentation, collision and Goffman in NOTE-710, and Chapters 1, 4 and 7 in full in NOTE-1432 (both Skimmed). An ethnography of US teenagers in 2004–2008: the dynamic is documented with interviews and examples, not measured, and the paradigm case, Stokely Carmichael’s two rhetorical styles, reaches the record secondhand through Meyrowitz, who is unread. Proposed because it rests on a skim and on unmeasured evidence. | Proposed |
| THEORY-407 | For a log-integrable linear cocycle over an ergodic probability-preserving system, vectors grow at finitely many exponential rates along an invariant flag, and for isometries of a proper metric space with integrable displacement the linear drift is detected by a horofunction, with no curvature assumed | Filip (2017), LIT-093, expository notes read in full in NOTE-078. Thm 2.2.6 is the Oseledets theorem, proved without Kingman; Thm 4.3.1 is the Karlsson–Ledrappier theorem, proved completely apart from cited measurable-selection results. Both are classical and not in doubt. The notes’ own renditions of two other steps are flawed: Prop. 3.4.8(iii) is mis-stated, and the §5.3 tracking proof misapplies its lemma, so the Karlsson–Margulis and Kaimanovich forms should be cited to their originals. The hypotheses are ergodic stationary sampling and N → ∞. | Active |
| THEORY-408 | In a one-locus model with non-overlapping generations, random mating and weak selection, gene frequencies change as if each individual maximized its inclusive fitness, so a trait that costs its bearer spreads only if its effect on relatives exceeds 1/r times the cost; the increase of mean inclusive fitness is proved only for traits whose total effect on others is not negative | Hamilton (1964), Part I, LIT-497, read in full in NOTE-401. Each effect an individual causes falls partly on genes identical by descent with its own (weight r) and partly on others, which only dilute. So selection tracks inclusive fitness. The threshold is written −k > 1/r (§5), not rb > c: “more than two brothers, or four half-brothers, or eight first cousins”. The maximization theorem needs non-negative total effects on others; for harming traits the change only points uphill. r is exact only for loci not under selection, and Hamilton could not bound the error (§4). | Active |
| THEORY-409 | A person’s mind is normally a system of parts that take protective roles, managers, exiles and firefighters, forced on them by experience and not part of their nature; beneath the parts is a Self, distinct from all of them and present from the start, which appears with calm, curiosity and compassion when the parts step back and which heals by leading the system | Schwartz, LIT-579 (the IFS Institute’s “Evolution” essay, read in NOTE-453) and LIT-591 (Internal Family Systems Therapy, chapter 1 only, NOTE-457, Skimmed). The model in its developer’s words. Its evidence is clinical: clients’ reports of parts, the founding “step back” case, and “hundreds of clients for more than two decades”. No study is reported in either source, and the book’s research chapter was not read. It is filed as the account IFS offers, not as an account the record has tested. | Proposed |
| THEORY-410 | Brain–computer interface decoding does not show intentions to be causes distinct from their neural realisers: what is many-to-one realised there is a coarse cortical variable over single-neuron patterns, and each intention matches one value of it, so under proportional difference-making the evidence fits identifying the intention with that variable | Pernu (2018), LIT-147, read in NOTE-091. A conceptual argument that turns on an empirical premise the paper asserts and does not examine: that each intention corresponds to one ensemble-average firing value. Real decoders are not simple averages, and whether the mapping holds across sessions or subjects is not checked. It is scoped by its own footnote 1 to difference-making with proportionality. | Proposed |
| THEORY-411 v2 | In Sen’s capability approach the weighting of functionings is left to public reasoning, and evaluation can still guide action without agreement on weights: where every weighting in an agreed range, or every view by its own argument, ranks one option above another, that ranking holds, so the approach is deliberately incomplete and yields a partial ordering | Wells, IEP “Sen’s Capability Approach” (2012), LIT-284, read in NOTE-257, §3b; with Sen (1979), LIT-289 (NOTE-258), whose index is already “a partial ordering” supplemented by “conventions of relative importance” (p. 219). The arithmetic is trivial and holds; the attribution of the intersection and ranges-of-weights devices to a particular Sen text is not given by the IEP, and the SEP (LIT-283) says Sen “has never explained in detail” how selection should be done. | Proposed |
| THEORY-412 v2 | Driven matter tends toward states that look adapted to the drive, with no replication needed: of two outcomes of a system driven by a fixed external field, equal in internal entropy and in the probability of reversal, the likelier is the one whose formation absorbed work from the drive and dissipated it more reliably | Perunov, Marsland & England (2014; Phys. Rev. X 2016), LIT-518, read in NOTE-416, on England’s macrostate relation (LIT-515). The log-odds of two driven outcomes decompose exactly into an internal-entropy term, a reversal term and Ψ − Φ = −ln⟨e^{−βΔQ}⟩. The “tendency towards adaptation” needs the first two held equal. The paper does that only in two single-particle hopping models, argues the many-body case, and reports a driven-chemistry simulation without showing it. The reading judged the claim too weak to source a THEORY; it is filed as Proposed for that reason. “Adapted” here means absorbing the drive’s work, nothing more. | Proposed |
| THEORY-413 | ’Unit of selection’ names four separable roles, interactor, reproducer, manifestor of adaptation and beneficiary, and being an interactor at a level does not require engineering adaptations at that level, so showing that a level lacks them does not show it is not a unit of selection | Lloyd’s SEP entry (2005, revised 2024), LIT-160, read in NOTE-184. Her own programme, stated in the first person, and advocacy as well as a map. The four-question anatomy is the firm part. The diagnosis that conflating interactor and manifestor is “the most common error” is asserted, not counted. Its rulings on kin and group selection, the cheater problem and the Price equation are one school’s, not consensus. | Proposed |
| THEORY-414 | Institutions are rules in equilibrium, correlated equilibria of coordination games with several equilibria that the players represent to themselves as rules, and a constitutive rule ‘X counts as Y in C’ is a regulative rule split by a coined term into a base rule and a status rule, so the term adds a name and cognitive economy but no new kind of fact | Hindriks & Guala (2015, online 2014), LIT-481, read with the authors’ reply to six commentators in NOTE-395. The equilibrium half is a clear synthesis of Lewis, Aumann, Aoki and Greif. The reduction of Searle’s constitutive rules is worked once, for a toy first-occupancy property, and asserted in general; it depends on a reading of “collective acceptance” loose enough to make the “counts as” biconditionals hold by construction, and on extensional equivalence of behaviour. The reply adds that a right is a bundle of others’ regulative obligations. | Proposed |
| THEORY-415 | Nothing has all four marks that qualia are said to have, being ineffable, intrinsic, private and directly apprehensible, because neither the subject nor an outside tester can tell a change in a quale from a change in the subject’s reactions to it; what is real in their place is the practical ineffability and idiosyncrasy of information-rich property detection | Dennett (1988), LIT-433, read in full in NOTE-357. Argued by fifteen intuition pumps, not by proof, and the author says so. The central step rests on a stipulation that two surgeries, or two adaptation stories, produce identical introspective effects. NOTE-357 filed no THEORY because the record does not hold the replies (Shoemaker 1981, Block 1980); this account states the claim as the reading supports it and leaves it Proposed for that reason. Its “there simply are no qualia at all” is a tactical choice of words by the author’s endnote 2. | Proposed |
| THEORY-416 | Quantum thermodynamics has at least four inequivalent notions of work, the ensemble average, the two-point-measurement random variable, the ε-deterministic single-shot work content and the resource-theory work, which answer different operational questions; only the two single-shot optima coincide, by identification of formulas and for energy-diagonal states | Vinjanampathy & Anders (2015/16), LIT-010, read in full in NOTE-011. The review’s one synthesis (§5.2, §7) sets four definitions side by side: ⟨W⟩ = ∫tr[ρḢ]dt (Eq. 2), W = E_m^(τ) − E_n^(0) (Eq. 24), A^ε ≈ −kT ln(Z_Λ*/Z) (Eq. 49) and w^max_ε = F^min_ε(ρ_S) − F(τ_S) (Eq. 50). Only the last two agree, and that agreement is an observation that two published formulas match, for states diagonal in energy. It is an informed judgement of a 2016 snapshot, not a theorem that the notions cannot be unified. | Proposed |
| THEORY-417 | ’Personal identity’ names several largely independent questions, among them who one is (characterization), what a person is, what it takes for one to persist, how many of us there are and what matters in survival; the persistence question concerns numerical identity, which ‘remaining the same person’ in the characterization sense presupposes, and posing it as ‘a person at one time and a person at another’ assumes that we are persons essentially | Olson (2002; rev. 2023), LIT-454, read in NOTE-374. Seven questions: characterization, personhood, persistence, evidence, population, personal ontology and what matters. The distinctions are conceptual and the record holds them as stated. They do not say which answer to any of the questions is right; the entry’s own answer, animalism, is argued in other sections and is not part of this account. The self is set aside by the entry, so the map does not cover the self literature. | Active |
| THEORY-418 v3 | A collective becomes a new level of individuality, on this sketch, only when collaboration toward a shared goal, rather than coordination or cooperation, organizes it and some core interactions have become generatively entrenched and, as the paper asserts without deriving it from entrenchment, it has organizational closure; such a community can then be reproduced only by exporting an organized sample of its roles and interactions, not of its members alone | Griesemer & Shavit (2023), LIT-188, read in NOTE-173. A conceptual sketch, so called by its authors, with no model, data or operational criteria. The paper’s two headline claims, that it describes evolutionary transitions non-circularly and that individuality is a special case of collectivity, appear only in the abstract and are not argued. Stage 3 is defined by a shared goal (§1), and §3 makes sustaining the community “a focal goal of every participating member”, which presupposes the group. The one argued conclusion, that inheritance at the new level evolves “in tandem”, is hedged and in tension with §2. | Proposed |
| THEORY-419 v2 | In a structural causal model of autonomous equations, with intervention do(X = x) defined, as Pearl defines it, as a surgery that deletes X’s own equation, sets X to x and solves the rest, and with observing X = x violating no equation and amounting to ordinary conditioning, models that agree on every observational distribution can disagree on the effect of an intervention, and in a structural equation y = βx + ε the coefficient β is the rate of change of E[Y | do(x)], which equals the regression slope of Y on X only when X is uncorrelated with ε | Pearl (2009), LIT-894, skimmed in NOTE-696 from four excerpts the author posts: the contents, the second-edition preface, §§5.3.2–5.4.1 and the Epilogue, 46 of some 480 pages. The account is well established and the excerpts state it in full; Proposed because it rests on a skim. The surgery needs autonomous equations and a diagram saying which equation belongs to which variable. The excerpts state the three rules of the do-calculus without derivation, and contain no three-level hierarchy of association, intervention and counterfactual. | Active |
| THEORY-420 | In trained transformers, zeroing a decile of a weight matrix’s singular values does damage that falls monotonically with their size in square matrices, whose random-matrix null reaches zero, but not in rectangular ones, whose null has a positive lower edge: there the smallest decile is never the least damaging and can be among the most | Staats, Thamm & Rosenow (2024), LIT-856, read in NOTE-659. Freshly initialised matrices of BERT, Pythia and Llama follow the Marchenko–Pastur law; trained ones depart from it above the bulk, and, in rectangular matrices only, below it. Zeroing Llama-3 8B’s smallest Down-Projection decile leaves 2.0% on GSM8K from 43.2%, worse than every decile but the largest, while the same decile of the square Attention-Output leaves 40.0%. Whether the below-bulk outliers are what carries the damage is not tested: the decile mixes them with the lower bulk, and overlap with the input’s principal directions and ablation importance disagree for several matrix types. | Active |
| THEORY-421 v2 | In HGCN embeddings of two synthetic 3-ary trees trained for link prediction or node classification, distance from the origin is only a partial reading of hierarchical level: the root is not innermost (distance 1.8–3.3 against a minimum of 1.2–2.4) and level order is recovered for 69–75% of node pairs; a loss built only on pairwise distances leaves the origin arbitrary | Yang, Zhou, Ying, Chen & King (2023), LIT-871, read in NOTE-669. On two synthetic 3-ary trees of eight levels, HGCN leaves the root at hyperbolic distance 1.8–3.3 from the origin where the minimum is 1.2–2.4, the distances are roughly normal rather than leaf-heavy, and radius orders true levels for 69–75% of 5,000 random pairs. Recentring on the centroid plus an outward push raises that to 75–84%. The diagnosis rests on one architecture, two synthetic trees and one table without variance, and the paper does not separate a real failure to order levels from the origin’s arbitrariness under losses that see only pairwise distances. | Active |
| THEORY-422 | In the standard formal models of group learning, no communication network is best for every epistemic problem: costly transmission favours minimally connected or star networks, pooling of estimates by averaging favours regular networks, and learning by trying in bandit problems can favour sparse ones, so a group’s network cannot be judged until its learning problem is known | Zollman (2013), LIT-716, a survey read in NOTE-567. Each result it gathers is proved or simulated in its source (Bala and Goyal, Jackson and Wolinsky, DeGroot, Hegselmann and Krause, Zollman). Under their idealisations the optimal structure changes with the problem, so neither “too little communication” nor unequal centrality is by itself an epistemic pathology. It is a claim about models: utilitarian optimality only, with fairness, robustness and the route to the optimum left out. | Active |
| THEORY-423 | Statements that are visibly false to anyone who checks, such as ‘long-term’ for a three-day study or ‘assault’ contradicted by video, persist in science, paid testimony and official statements when the community that hears them accepts them as terms of art and attaches no cost to them, so that those willing to make things up gain over those who are not | Gelman (2025), LIT-014, a blog post its author calls a rant, read in NOTE-019. An incentive account from three to five anecdotes: false phrasing helps a case, a channel (journals, courts, media) carries it, insiders treat it as a term of art, and nothing follows, so by a Gresham’s-law dynamic honest argument loses. Nothing is measured, and the post is inconsistent on whether the speakers know they are lying. | Proposed |
| THEORY-424 v2 | Mutual-information measures of individuality that read a system’s next state off its present one measure association, not propagation: I(S_{t+1}; S_t) can be positive when the environment alone drives the system, and conditioning on the environment does not recover the interventional quantity, which can be zero where the conditional measure is one bit | Bourrat (2024), LIT-005, read in NOTE-027, against Krakauer et al.’s (2020) measures. A* = I(S_{t+1}; S_t) is confounded when the environment is a common cause (his Fig. 2), and his interventional  = I(S_{t+1}; Ŝ_t) is zero there. His claim that  equals Krakauer’s conditional A = I(S_{t+1}; S_t | E_t) is false in general: NOTE-027’s XOR system has A = 1 bit and  = 0.  itself depends on an intervention distribution the paper leaves open, and neither it nor the paper’s two ETI criteria is computed on any system. | Active |
| THEORY-425 | A connecting path trained only on clean data keeps only the behaviour the clean data ask for: between two backdoored or error-injected image classifiers, models near the ends of such a path keep most clean accuracy and lose the attack, and a path flat in ordinary loss can carry a barrier in adversarial loss that tracks the input Hessian’s top eigenvalue | Zhao, Chen, Das, Ramamurthy & Lin (2020), LIT-668, read in NOTE-530. A quadratic Bezier path trained on 50–2,500 clean samples between two backdoored VGG-16s on CIFAR-10 has, at t = 0.1, 88% clean accuracy and 1.1% backdoor success with 2,500 samples, and 63% and 2.5% with 50; injected weight errors fail at every point of such paths. Paths trained with the standard loss between regular and adversarially trained models are flat in standard loss with a PGD-loss barrier correlated with the input Hessian’s top eigenvalue (0.71–0.88). The proposition offered for that correlation rests on an assumption that would remove the barrier. | Active |
| THEORY-426 v2 | Evaluating expected free energy recursively over the beliefs an agent would hold after each plausible outcome makes active inference a pruned tree search over belief states, formally analogous to Bellman recursion; in single deterministic runs on a T-maze and an 8 × 8 maze it planned through short-term costs that agents with a shorter horizon did not; that the pruning keeps deep search tractable beyond toy problems is argued, not shown | Friston, Da Costa, Hafner, Hesp & Parr (2020), LIT-577, read in NOTE-454 as prose: the equations were not recoverable from the text layer. The recursion is a construction (strong). That it plans through costs rests on single deterministic runs of a T-maze and an 8 × 8 maze. The title keeps that scope. Active as a report of the construction and of those runs; the general form is THEORY-1245, Proposed. | Active |
| THEORY-427 | For gradient matrices of rank at most r, the Kronecker product of the square roots of the accumulated row and column gradient second moments dominates the full-matrix AdaGrad statistic up to the factor r, so preconditioning each side of a weight matrix by a fourth root, as Shampoo does, preconditions at least as strongly as full-matrix AdaGrad and has O(√T) regret for convex Lipschitz losses | Gupta, Koren and Singer (2018), LIT-621, read in NOTE-480. Lemma 8 is pure matrix analysis (operator monotonicity of the geometric mean); Theorems 7 and 10 give regret √(2r) D Tr(L^{1/4}) Tr(R^{1/4}), O(√T) when the spectral norm of the gradients is at most 1. Proved, in online convex optimisation, with D uncontrolled because the implementation omits the projection. Nothing here is a result about non-convex training; the deep network curves are four runs without seeds. | Active |
| THEORY-428 | A protest performed bodily inside a civic ritual can contest the ritual in its own grammar, keeping the ritual’s reverence for its ideal while rebuking its present object, which is incivility in the Confucian sense of disruption aimed at harmonization; the reading of the gesture and the claim that its uptake makes it sagely are asserted | Walsh (2021), LIT-209, read in NOTE-164 from the accepted manuscript. Comparative-philosophy interpretation of Kaepernick’s kneeling during the U.S. anthem. Its textual base is strong: classical Confucianism licenses incivility aimed at harmonization (after Kim 2011). Its own addition, that such incivility can be bodily and within the ritual, is moderately argued. That kneeling means reverence rather than defiance, and that sagely authority is uptake by others, are asserted, and the paper gives no criterion separating sagely uptake from virality. | Proposed |
| THEORY-429 | Institutions are the humanly devised formal and informal constraints on interaction; with technology they fix the costs of transacting, organisations arise to exploit the opportunities they offer, and an economy grows when its framework rewards productive rather than redistributive activity, while increasing returns to the institutional matrix make frameworks path dependent, so that economies with different frameworks diverge and need not converge | North (1991), LIT-489, read in full in NOTE-392. A programmatic essay, not an argument. The definition is stipulated; the game-theoretic motive for third-party enforcement is one paragraph; the evidence is narrative history from secondary sources, with the staged sequence of exchange disclaimed as history (n. 1); path dependence is carried over from Arthur and David on technology by analogy. It leaves open why informal constraints bind, which is the question Hindriks and Guala put to rules accounts. | Proposed |
| THEORY-430 | A real hyperplane arrangement in ℝⁿ has (−1)ⁿχ(−1) regions and (−1)^rank χ(1) bounded regions, where χ is the characteristic polynomial of its intersection poset, so these counts depend only on which hyperplanes meet and in what dimension, not on the shapes of the regions | Stanley (2006), LIT-355, lecture notes read in full in NOTE-313, with Lectures 1–2 and 6 read closely. Zaslavsky’s theorem (Thm 2.5) is proved twice, by a deletion–restriction recurrence and by Euler characteristic; the bounded-region half has two unanswered “[why?]” steps in the first proof and an omitted fact in the second. Faces of every dimension are counted by Möbius values (Thm 2.6). The notes never use “topes” or “covectors”, and do not cite Zaslavsky’s own texts. A region is fixed by its side of each hyperplane only implicitly (p. 89). | Active |
| THEORY-431 | For classical systems with Markovian, microscopically reversible dynamics, the entropy production of a trajectory obeys an exact finite-time symmetry against the time-reversed process, P_F(+ω)/P_R(−ω) = e^ω, wherever ω is odd under reversal; Jarzynski’s work equality and the mean second law follow as corollaries, and the symmetry constrains fluctuations, not which steady state a system selects | Crooks (1999), LIT-522, read in NOTE-413, with Jarzynski (1997), LIT-517 (NOTE-417), and Seifert’s review (2012), LIT-523 (NOTE-420). The work equality ⟨e^{−βW}⟩ = e^{−βΔF} holds at any switching rate, and Crooks derives it from a trajectory-level entropy-production theorem; Seifert derives every known theorem of the kind from one master theorem. These are exact given their premises. They are not proofs of the second law, since the dynamics build irreversibility in, and they say nothing about extremum principles for steady states. Their practical reach is work fluctuations of order k_BT. | Active |
| THEORY-432 v2 | In Lévi-Straussian analysis of myth the group of transformations is not given by the material: which variants count as transforms of which, and by what operation, is cut by the analyst from a continuum, unlike transformations that develop an initial form by a rule, and the computational encodings of the method confirm this by taking the analyst’s table of oppositions as input | Descola (2016), LIT-822, read in NOTE-641, distinguishes a Goethean regime (variants developed from an initial form by a rule, as in kinship) from a Thompsonian one (deformation between given forms, as in myth), and cites Lévi-Strauss’s own admission that the myth group is a continuum the analyst cuts. Santucci, Doja and Capocchi (2020), LIT-807, read in NOTE-632, implement the method and concede that every inverse or opposite term “is not obtained from the software system”. A keynote’s argument and a software paper’s concession; no test of the claim exists in the record. | Proposed |
| THEORY-433 | Whether a machine thinks is best replaced by whether a digital computer can play the imitation game as well as a man, because the reasons for withholding thought from a machine that does would equally withhold it from other people, whose thinking we also infer from what they say; the objections from consciousness, mathematical limits and informality of behaviour fail on that test or rest on unproved premises | Turing (1950), LIT-394, read in NOTE-355. The imitation game is offered in place of a definition of thinking, not as a test of it, and Turing says he has “no very convincing arguments of a positive nature”. The account’s force is the other-minds parity of §6.4, which assumes, as §2 states and does not argue, that the machine’s best strategy is to answer as a man would; a machine built to imitate human output is the case that assumption does not cover. It makes no claim about consciousness. Proposed, and a rival of Block’s psychologism. | Proposed |
| THEORY-434 | Rawls’s theory of justice is transcendental only in the formal sense that its principles state when a society is perfectly just; it already yields comparative judgements, prescribes no single set of institutions and sits inside a revisable reflective equilibrium, so Sen’s case against ‘transcendental institutionalism’ misses Rawls, and what it shows is that the theory is incomplete, not that a new paradigm is needed | Valentini (2010), LIT-290, read in NOTE-262 from the 2010 working paper, with Zwolinski’s review (LIT-286, NOTE-261), which agrees with her on what the book says and disagrees on its worth. A one-sided Rawlsian rebuttal: two points are strong as textual claims (Rawls’s principles are comparative; his method is reflective equilibrium), the rest moderate. The claims about The Idea of Justice are second-hand, and Sen’s own reply is unread. | Proposed |
| THEORY-435 | In Moral Foundations Questionnaire responses, Care and Fairness are endorsed across the political spectrum, while Loyalty, Authority and Sanctity rise toward the conservative end, in every world region sampled | Graham, Haidt et al. (2013), LIT-499, read in NOTE-396, reporting large internet samples in twelve world regions; and Atari et al. (2023), LIT-500 (NOTE-398), with the MFQ-2 in 19 nations. The profile is robust as a description of self-report. It is a finding about what people say they weigh, mostly online, mostly English-speaking, and mostly WEIRD; and Purity, which carries the steepest gradient, fails cross-national invariance in the MFQ-2. | Active |
| THEORY-436 | Pain is a functional state of a whole organism, possessing a certain functional organisation as a probabilistic automaton, rather than a brain state, and this is the more plausible empirical hypothesis because one pain predicate applies to physically different organisms; the hypothesis keeps swarms out only by a stipulated condition that no pain-feeler has parts that separately possess the organisation | Putnam (1967), LIT-396, recorded as Skimmed in NOTE-335 from a course excerpt of the 1975 reprint, which carries the four-clause hypothesis verbatim; the original is Unavailable here. Proposed, and resting on that excerpt and on a result discussed throughout the literature the record holds. Clause (1) is empty by Putnam’s own admission, since everything is a probabilistic automaton under some description, and clause (3), the anti-nesting condition, is introduced with one motive, to rule out swarms of bees. The argument against the brain-state view is comparative plausibility, not evidence. | Proposed |
| THEORY-437 | When each agent’s feasible actions depend on the others’ actions, an equilibrium exists if every action set is a contractible polyhedron, every constraint correspondence has a closed graph with non-empty compact values, payoffs and the maximum-value functions are continuous, and every best-response set is contractible; convexity is not needed | Debreu (1952), LIT-067, read in full in NOTE-037. The theorem (p. 888) is proved by applying the Eilenberg–Montgomery/Begle fixed-point theorem to the product of best-response correspondences. A Remark reduces the continuity of the value function to a compact graph plus continuity (lower hemicontinuity) of the constraint. It is existence only, in finite dimensions with finitely many agents and real-valued payoffs. That it contains Nash’s theorem is asserted; the reduction is routine but not in the paper. | Active |
| THEORY-438 | The understanding deep networks reach is characteristically fractured: it can be real, by the test of stable tracking under structure-preserving perturbation, but it is symbolically misaligned, non-reductive, locally fractured, proxy-dependent and representationally fragmented, because the loss rewards any predictive patchwork and does not press it to unify | Freeborn (2026), LIT-131, read in NOTE-123. The Fractured Understanding Hypothesis is argued from four small demonstrations and cited literature, with no test of how common the five features are. The abstract names three features and §7.5 five. The paper also applies its own criteria inconsistently: its Othello verdict uses post hoc probes that it excludes from the agent. The definition of understanding it rests on is an explication, not a finding. | Proposed |
| THEORY-439 v2 | Given the same few demonstrations, temporarily updating a language model’s weights on them and then conditioning beats conditioning alone, most on tasks with structural rules or distribution shift and most when the update is trained in the in-context format: for models of 1–8B parameters, examples used as context and the same examples used as a training signal are not interchangeable | Akyürek et al. (2024; ICML 2025), LIT-796, read in NOTE-637. On BIG-Bench Hard with Llama 3.1 8B and 10 demonstrations over five seeds, zero-shot 40.9%, in-context 50.5%, per-task LoRA test-time training then in-context 57.8%; 12 of 27 tasks gain at least 2 points, and Boolean expressions falls. Training the update on leave-one-out in-context tasks beats training on bare pairs (57.8% against 51.5%). The update is discarded after each task, so it is as transient as a context. It is two benchmarks and one model family, and which task property predicts the gain is open. | Active |
| THEORY-440 | A democracy that breaks down under an elected incumbent need not become a dictatorship: elections, courts and a legal opposition can continue while the incumbent uses state power against opponents and tilts the field, giving competitive authoritarianism, in which competition is real but unfair and the decisive loss is the opposition that withdraws or never forms; Levitsky and Way forecast this for the second Trump term | Drezner (2025), LIT-022, an opinion column read in NOTE-001, which relays Levitsky and Way’s Foreign Affairs forecast largely by quotation and endorses it (“hard to disagree”) without independent argument. The concept of competitive authoritarianism is theirs and well established; the record holds it only through this relay. The forecast that US democracy will “likely break down” in the second term is rated weak in the reading, and the post’s index figures are second-hand. | Proposed |
| THEORY-441 | In spatially compact vacuum general relativity the Hamiltonian vanishes, so time is represented by no flow on a symplectic space and change by no functions on a space of states; this problem of time does not come from the 3+1 split, is absent from asymptotically flat general relativity, and does not show change to be illusory | Belot (2007), LIT-122, read in NOTE-118. A formal, not rigorous, derivation in the covariant phase-space formalism, with standard results cited. The vanishing Hamiltonian and the covariant derivation are strong; the canonical isomorphism of the reduced spaces is “presumed”; the claim that an artificially covariant theory escapes is hedged (“I think”). It is classical only. It diagnoses the problem and does not solve it. | Active |
| THEORY-442 | Where the non-epistemic consequences of error are foreseeable, sound scientific reasoning requires weighing them in the internal choices that carry inductive risk, and non-epistemic values then enter legitimately only indirectly, through the costs of error, never as reasons to think a claim true | Douglas (2000), LIT-139, read in NOTE-145. The normative half of the paper. It rests on a premise the paper declares “beyond the scope” and does not argue, that scientists are morally responsible for foreseeable consequences of error (p. 563). The direct/indirect line is drawn sharply in the conclusion but only sketched, and the reply that scientists could report uncertainty instead of accepting is not engaged. | Proposed |
| THEORY-443 | Being a biological individual is not being an organism: evolutionary (Darwinian) individuality and physiological individuality come apart, and each is found among parts of organisms and groups of organisms as well as among organisms, so a part or a group can be an individual of one kind and not the other | Wilson and Barker (SEP, 2007; substantive revision 2024), LIT-168, read in NOTE-114. That organisms are not the only biological individuals is argued from examples; that evolutionary and physiological individuality is the most recognised distinction is a survey judgement. The nine-region framework that places each case is the authors’ own and tentative, and its figures draw as disjoint the categories the text says overlap. It offers no criterion of parthood and leaves holobionts open. | Proposed |
| THEORY-444 | To mean something by an utterance, in the non-natural sense, is to intend it to produce an effect in an audience by means of the audience’s recognition of that intention, where the recognition is meant to be a reason for the effect and not merely its cause; an intention to produce the effect, or to have it recognised, is not enough | Grice (1957), LIT-1042, read in full in NOTE-735. The analysis is reached by counterexamples to weaker conditions (the handkerchief, Herod and Salome, the photograph against the drawing) and stated “roughly”. It is an analysis of speaker meaning on an occasion, not of illocutionary acts, and its extension to timeless and sentence meaning is “a first shot” with the red light admitted as awkward. Strawson’s watcher case (LIT-1043) shows its three intentions are not sufficient. | Proposed |
| THEORY-445 | A network built from group correlations over a discrete split group of plane symmetries, pointwise nonlinearities and coset pooling is equivariant to that group by construction, through the regular representation alone: the group is fixed before training and built into the weight sharing, not found in the data | Cohen & Welling (2016), LIT-314, read in NOTE-288. G-correlation commutes with the left action of G by the change of variables h → uh (eq. 12), and so do pointwise nonlinearities and pooling over cosets, up to edge effects and for rotations that are symmetries of the grid. Matched-parameter p4 and p4m layers lowered rotated-MNIST error from 5.03% to 2.28% and plain-CIFAR10 error from 9.45% to 6.46%. The paper uses no irreducible representations, characters or Fourier analysis, learns nothing about which symmetry the data have, and does not separate the effect of equivariance from the changed channel structure. | Active |
| THEORY-446 | Organism–environment reciprocal causation, taken diachronically, unrolls into an acyclic sequence of organism, environment and experienced-environment states joined by interventionist arrows; on that representation each niche-construction type has a characteristic causal pattern, and multi-species cases come apart only if organism and environment are kept distinct | Baedke, Fábregas-Tejeda & Prieto (2021), LIT-110, read in NOTE-111. A conceptual and visual model, worked by example for each type of niche construction and for two multi-species cases. There is no formal semantics, no completeness result and no empirical test; formalization is deferred. It sets synchronic co-constitution aside rather than refuting it, and the claim that the boundary is an “epistemic necessity” is stronger than the argument, which shows only that the model can draw one usefully. | Proposed |
| THEORY-447 v2 | Granted that a person survives a brain transplant and that half a brain would do, each product of a division stands in all that matters in ordinary survival, so what matters is not identity, which is one-one and all-or-nothing, but psychological relations that can branch and come in degrees | Parfit (1971), LIT-447, read in NOTE-378, with the fission dilemma as Olson’s survey states it, LIT-454 (NOTE-374). The division argument is strong given its premises, and the premises are stated: brain-transplant survival is assumed, not argued. It does not say that connectedness matters more than continuity, which Parfit asserts for lack of space, or that a copy or a transcript is a survivor: the dependence q-memory needs is left “(whatever that is)”. | Proposed |
| THEORY-448 | On a substance ontology, a gestated foster that is part of the pregnant organism either is no substance, so that mammals begin at birth and the foster is not the later baby, or is part and substance at once, which leaves no consistent count; a process ontology keeps both parthood and foster–neonate identity, at the price of a count between one and two that it does not define | Meincke (2021), LIT-142, read in NOTE-115. The critique of the Parthood View under substance ontology holds on its own and is the paper’s firm contribution. The positive view rests on five process-biology premises assumed for the sake of argument, and is programmatic by the paper’s own word; “something in between one and two” has no formal content. It keeps parthood rather than rejecting it, and it draws no ethical conclusion. | Proposed |
| THEORY-449 | If sentience comes in degrees, plants may be faintly sentient, and moral status is graded by degree of sentience, then plants have a partial moral status so low that animal interests outweigh theirs in most cases; all three premises are assumed, and the second rests on contested, second-hand evidence | Terrill & Veit (2024), LIT-193, read in NOTE-120. The conditional is valid; its premises A1 (graded sentience), A2 (plants may be quasi-sentient) and A3 (status graded by sentience) are assumed, and A2 is supported mainly by a popular book and commentaries. The paper gives no scale and no aggregation rule. It should not be cited as evidence of plant sentience, and the second author’s later work leans against plant consciousness. | Proposed |
| THEORY-450 | Across 1,176 premodern archaeological sites, the house-size Gini rises only weakly with the number of levels of political hierarchy and with polity population, and the spread of Gini widens with scale: scale raises the ceiling on domestic wealth inequality without setting its level | Feinman et al. (2025), LIT-087, read in full with its SI in NOTE-049. Bivariate fits on the GINI project’s site-level file (47,019 houses): levels of hierarchy give r² 0.16 (all sites), 0.22 (apex), 0.27 (sites with 50 or more houses); log polity population gives 0.11, 0.21, 0.08. The scatters fan out as scale grows, and the sites that reach Gini above 0.75 are autocratic apices of polities with three or more levels. The negative claim, that scale does not fix inequality, is what the record believes. The positive claim, that governance decides it, rests on an expert-coded index partly read from architecture and on a composite whose higher r² comes from summing two predictors; it is not part of this account. | Active |
| THEORY-451 | A singular causal claim, that C will contribute or did contribute to E in a particular setting, is warranted only by joint evidence on each step of the causal process there, its causal principle, its support factors and the absence of its derailers, which no single method supplies; a well-run RCT secures at most the study population’s average effect, and often not even that rigorously, and its result is not by its method evidence about any other population | Cartwright (2021), LIT-213, read in NOTE-161. The point that RCT results are not by the method evidence about another population (save under random sampling from it) is strong and standard. That no method or handful of methods can warrant a singular claim is argued from the diversity of facts a causal-process theory of change needs, with one illustrative case. That such theories yield reliable predictions is asserted, with no track record; the paper gives no method for weighing the evidence and little on transport. The critique of RCT rigour is internal to the author’s own reconstruction of “rigour”. | Proposed |
| THEORY-452 | A thing with many equally good candidate boundaries can be counted as one in two ways that cover each other’s failures: supervaluation makes ‘there is one cat’ true on every precisification though no candidate is definitely the cat, and counting by almost-identity, meaning extensive mereological overlap, makes it true enough where the candidates overlap almost completely | Lewis (1993), LIT-1015, read in full in NOTE-722. Two answers to Unger’s problem of the many, offered together. Supervaluation makes “there is one cat” super-true at the granted cost that nothing is super-truly the cat. Almost-identity, which is overlap and not similarity, makes the many candidates “almost one”. It is not transitive and its threshold is left undecided. Each covers a case the other fails: Fred’s house needs supervaluation, and supervaluation is natural only where the candidates differ little. It assumes semantic indecision, perdurance and no natural joint among the candidates. It has no metric, no dynamics and no threshold, so it is a precedent for counting by something weaker than identity, not evidence for any of the record’s claims. | Proposed |
| THEORY-453 | Basic physical objects can be nothing beyond the bearers of their relations: relations give them identity conditions wherever they discern them, and where nothing discerns them, as with entangled systems of one kind or points of a symmetric space-time, a primitive numerical diversity that is not a thisness suffices; general relativity’s tensor and fibre-bundle formulations fit this reading but do not require it | Esfeld & Lam (2008), LIT-895, read in full in NOTE-695. Moderate structural realism: relations require relata, but relata need no fundamental intrinsic properties, and objects and relations depend on each other with no priority. Its distinctive move is primitive numerical diversity, which it says gives no identity of any sort. The GR sections show interpretive fit, not entailment. Identity is equivocal between §1, where symmetric space-times need primitive diversity, and §2, where the metric “completely determines” structural identity; the one concrete construction cited works only without symmetries and breaks the general covariance the view rests on. The no-priority argument assumes three options are exhaustive. | Proposed |
| THEORY-454 v2 | Perception is constitutively iconic, nonconceptual and nonpropositional and cognition paradigmatically discursive, and percepts are put to cognitive use only inside a ‘cognitive envelope’, the global workspace read as conceptualisation, where working memory holds recoded, task-dependent abstractions rather than the percepts themselves | Block (2024), LIT-649, read in NOTE-498: the précis of his 2023 book, not the book. The main thesis is stated and its arguments are in the book, unread here. The working-memory half is the update: nine cited lines of evidence that working-memory representations differ from perceptual ones and are task-dependent abstractions (moderate). The rereading of the workspace as conceptualisation rather than consciousness is asserted, not argued against the consciousness reading. | Proposed |
| THEORY-455 | Every finite stochastic transition matrix on a configuration space equals the entrywise squared modulus of a complex matrix, unitary after dilation, so the Hilbert-space formalism can be written over any indivisible stochastic process as a non-unique representation; within that representation interference is the term by which the process fails to divide at an intermediate time, relative to the chosen configurations, and an ideal correlating environment restores divisibility | Barandes (2023), LIT-086, read in full in NOTE-080. Γ_ij = |Θ_ij|² = tr(Θ†P_iΘP_j) is an identity (Θ_ij = √Γ_ij works), and a unitary Θ on the original space exists only for doubly stochastic Γ. Interference is the cross-term of Eq. 43 against a would-be Markov factorization, and a perfectly correlating environment that then evolves separately makes the process divisible (Eqs. 45–56). The “emergent” Schrödinger equation is the definition of H, unitarity is a choice the claimed gauge freedom does not preserve, and the decomposition is relative to a configuration basis the paper never fixes. | Active |
| THEORY-456 | Iterating Ollivier–Ricci flow on edge weights lengthens edges between communities relative to edges within them, so a weight threshold can separate the communities; but the separation is proved only on symmetric clique graphs under the uniform neighbour measure, and there only by a constant factor for gateway edges, and on a two-block stochastic block model the method fails at an inter/intra ratio near 0.55, where other methods still recover the blocks and well short of the detectability threshold near 0.78 | Ni, Lin, Luo & Gao (2019), LIT-004, read in full with its SI in NOTE-006, which checked Lemma E.1 by linear programming and iterated the proof’s matrix. The flow w ← (1 − κ)d replaces each weight by the transport cost between the endpoints’ neighbourhoods; bridge edges, with few shared neighbours, are negatively curved and grow. Theorem 4.1 (α = p = 0, cliques G(a,b), a > b ≥ 2) shows only non-gateway intra-clique edges shrinking; gateway edges grow at the inter-community rate with a ratio k ∈ (0,1) from Maple. Experiments use α = ½, p = 2, which no theorem covers. The Kesten–Stigum figure is NOTE-006’s calculation. | Active |
| THEORY-457 | When people can choose their cooperation partners and have equal outside options, the stable division of jointly produced gains is in proportion to each partner’s contribution, and partner choice selects for a genuine sense of fairness as proportionality | Baumard, André & Sperber (2013), LIT-508, read in NOTE-407, with its 28 commentaries and Response. The pairwise result is cited from another paper; the extension to effort and talent is unproven by the authors’ own statement. The evidence is a reinterpretation of dictator, ultimatum, trust and public-goods results as allocation by entitlement. The authors disagree among themselves about whether purity, loyalty and kin care are moral at all. | Proposed |
| THEORY-458 v2 | Within the minimal self, the sense that a movement or a thought is mine and the sense that I am its source are distinct and come apart, as in involuntary movement and thought insertion; on Frith’s comparator model the sense of agency depends on a forward model that precedes action and ownership on sensory feedback, so failed forward monitoring would explain thought insertion and, by the same mechanism, why first-person reference ordinarily cannot misidentify its subject | Gallagher (2000), LIT-453, read in NOTE-377 from the preprint. A review with no new results: the dissociation and the comparator account are reported from Frith, Haggard and others, and the link to the immunity principle is Campbell’s argument, adopted and left conditional. It is about the minimal self, not the narrative self, for which the review’s own proposal is two paragraphs. It does not say which minimal self, embodied or reflective, the analysis concerns. | Proposed |
| THEORY-459 | Exact duality between two models is incompatible with ontological emergence of one from the other, reductive or not, because a duality is an isomorphism and ontological emergence needs a non-injective linkage whose interpretation does not commute; the two combine only when emergence runs beside the duality, as along the radial direction in AdS/CFT, through an approximate duality, or as merely epistemic emergence | De Haro & Butterfield (2025), LIT-199, §14.3, read in NOTE-178. A formal argument from equinumerosity and surjectivity, strictly proven for finite sets, with an argument on physical grounds for the infinite case (fn. 57). Emergence here is novel reference in the domain of application, a semantic condition, not an information measure. AdS/CFT is the exception only to incompatibility with non-epistemic emergence, not to “not indicative”: on a theoretically equivalent reading, its “emergent gravity” “cannot be understood as ontological emergence”. | Proposed |
| THEORY-460 | Every leading reason to deny consciousness to current large language models except biology names a missing feature, recurrent processing, a global workspace, unified agency, world and self models or senses and embodiment, that engineering could add, so the case against current models is much stronger than the case against their extended successors; the one possibly permanent objection, biology, is the one the argument sets aside | Chalmers (2023), LIT-411, read in full in NOTE-345. A classification of objections as temporary or permanent, argued by naming simple systems that have each feature. The credences that follow, under 10% for current models and 25% or more for conscious extended models within a decade, are illustrative by the author’s warning, multiply stipulated factors under a disclaimed independence assumption, and depend on “mainstream assumptions”. Biology is set aside with a reference to earlier work. It adds no evidence about any model. | Proposed |
| THEORY-461 | If a substantial class of mental states, interoceptive, affective, perceptual and bodily-agentive, depends on an animate body, then today’s text-only chatbots lack them and their self-ascriptions of such states are systematically untrue, and users can engage them without false belief by make-believe, as a new kind of interactive, self-involving and blended fictional character | Roberts (2026), LIT-207, read in NOTE-157. The anti-realist half is a valid conditional whose antecedent, moderate embodied cognition, is assumed at prima facie strength. It covers body-dependent states only; footnote 8 allows realism about the chatbot as a disembodied thinker, so belief and reasoning are untouched. The fictionalist half shows the attitude permissible and apt, not required, and offers no evidence that users hold it. It is not a general denial that chatbots have minds. | Proposed |
| THEORY-462 v2 | If commonsense knowledge includes defaults that later evidence displaces, a monotonic logic, in which an added axiom can never remove a theorem, cannot represent that displacement as it stands; Minsky’s further claim, that no logistic system, one that separates propositions from general laws of inference, can carry commonsense knowledge even once repaired, is asserted, not shown | Minsky (1974), the frames memo, LIT-410, read in NOTE-337. Its appendix argues that “logistic” systems fail for commonsense on five counts, of which monotonicity is a correct observation about classical logic. That no repair is possible is asserted (“I think such attempts will continue to fail”), and consistency being undesirable is argued by analogy. The reading says the memo is a source of hypotheses, not evidence; this account takes from it only the half that holds by definition and marks the rest as the memo’s claim. Active as the definitional half and a report of how the memo supports the rest; the further claim is THEORY-1239, Proposed. | Active |
| THEORY-463 | In classical statistical mechanics a strictly irreversible approach to equilibrium cannot come from the isolated Hamiltonian dynamics alone: the fine-grained Gibbs entropy is constant and bounded systems recur, so each account surveyed either weakens the target to typical or long-run behaviour or adds something from outside the dynamics | Frigg & Werndl (2023), LIT-114, the SEP entry, read in NOTE-103. The impossibility half rests on standard consequences of Liouville’s theorem, time-reversal invariance and Poincaré recurrence. The classification half is the survey’s: it is stated account by account, not argued as a general result. The entry is classical only, excludes the direction of time, and reports rather than settles the disputes about each repair. | Active |
| THEORY-464 | In the ethical questions that seem to turn on whether someone is the same person, among them prudential concern, responsibility, abortion, advance directives and the separateness of persons, the relation that decides is usually not numerical identity but one that comes apart from it, so the metaphysics of persistence constrains these questions and rarely settles them | Dufner (2025), LIT-130, the SEP entry that replaced Shoemaker’s, read in NOTE-166. A survey that takes no side; the account is the reading’s synthesis of what it reports, correcting a seeded summary that said the metaphysics “jointly settle” the ethics. It does not say identity never matters: uniqueness may matter for positional goods, and biological views support prohibiting abortion more strongly than psychological ones, without forcing it. | Proposed |
| THEORY-465 | Being reproduced does not entail reproducing: genes of multicellular organisms, like hearts, are reproducees with little reproductive autonomy and differ from hearts in reproductive causal control, and material overlap between parent and offspring is required of reproducers, which are whole life cycles, but not of reproducees | Bourrat (2025), LIT-157, read in NOTE-100. A definitional framework with no model or data. Both measures are recipes and neither is computed. The proxy for autonomy (conditional mutual information) measures resemblance given the environment, not the range of backgrounds the definition names, and the two recipes given for it differ. The overlap claim rests on a premise shown only for retroviruses, and the conclusion’s “necessarily” outruns it. | Proposed |
| THEORY-466 | Among contestants of equal prowess with dangerous weapons, individual selection can favour conventional fighting backed by retaliation: an escalating Hawk is not evolutionarily stable, Retaliator is at most neutrally stable because Mouse ties it, and in a contest settled by persistence alone no fixed persistence is stable while an exponential mixture is | Maynard Smith & Price (1973), LIT-505, read in full in NOTE-404. A simulation of five strategies, 2,000 contests per pairing, shows that “limited war” can be favoured by individual selection, without benefit to the species. The paper calls Retaliator an ESS “though Mouse does equally well”, which fails its own second condition. There is no Hawk–Dove game, no “dove”, no difference in prowess and no ownership, so it is not the source of display, deference or owner–intruder conventions. | Active |
| THEORY-467 | Rule-consequentialism that ranks codes by the expected good of teaching them to, and having them accepted by, new generations does not collapse into act-consequentialism, because teaching and internalisation costs favour codes simpler and less demanding than act-by-act optimisation, which therefore sometimes require sub-optimal acts | Hooker, SEP “Rule Consequentialism” (2003, revised 2023), LIT-198, read in NOTE-160. The view’s leading defender argues that the collapse objection fails once codes are ranked by the costs of teaching and internalising them, plus the assurance and temptation effects of exception clauses (§8). The premises about human nature (children’s partiality, per-rule cognitive cost) are asserted, not evidenced, and the incoherence reply holds only on the reflective-equilibrium route. An advocate’s survey, argued and not tested. | Proposed |
| THEORY-468 | Morality is the set of solutions to recurrent problems of cooperation, so each of the seven cooperation problems game theory identifies yields a moral domain valued in every culture, and behaviour unrelated to cooperation is morally neutral | Curry (2016), LIT-503, read in NOTE-408, with its two tests, LIT-047 (NOTE-034) and LIT-496 (NOTE-412). The positive half has support: the seven are described as good wherever ethnographers record them, and questionnaire items for them form seven factors. The negative half, that nothing else is moralized, is the theory’s own stated prediction (p. 40). No study in the programme has tested it blind, and where non-cooperative items appear, the programme’s own data show them moralized. | Proposed |
| THEORY-469 | Because persistence (mean absolute fitness at least 1) and selection (fitness differences) are logically independent, niche construction theory’s evolutionary niche, read externally as the factors producing fitness differences in a population, differs in extension from the realized population ecological niche even after unit and modality are matched, so it is not a simple translation of Hutchinson’s niche | Trappes (2021), LIT-169, read in NOTE-155. The non-identity follows from a conceptual argument the reading grades strong. The three kinds of case that populate the gap are weaker: habitat degradation rests on a projected persistence failure, commensalism on one field study after the author’s first candidate failed, and non-limiting resources on a “possible example”. The result is scoped to Odling-Smee, Laland & Feldman’s 2003 niche concept and to the externalist reading of selection pressure. It does not say the two niches differ much; they “still coincide to a large extent”. | Active |
| THEORY-470 v3 | Platform decay of the enshittification kind is caused not by a change in the character of those who run platforms but by the weakening of four constraints that used to discipline them, competition, regulation, interoperability and the bargaining power of tech workers, so it is reversible if those constraints are durably restored | Doctorow (2024), LIT-033, the crib of a DEF CON talk read in NOTE-041. It keeps the three-stage cycle of THEORY-150 and adds a cause: “Not because they used to be better people, but because they used to be subjected to discipline.” Argued from examples chosen after the fact, with no counterfactual; most figures are unsourced, and the text misstates the court in United States v. Google and the legal form of the EU Digital Markets Act. | Proposed |
| THEORY-471 | Psychological states are not the machine-table states of an organism’s unique best description as a probabilistic automaton, because some are never occurrent, several hold at once, there are indefinitely many and they contain one another, none of which a machine-table state can be; this leaves open that they are computational states of such a system | Block & Fodor (1972), LIT-641, read in NOTE-491. Five independent arguments against the machine-state identity theory, each with a stated escape that keeps functionalism: dispositions with no occurrent state, simultaneous states, too-fine individuation, productivity and constituent structure. They refute the machine-table clause, not functionalism. The paper’s remaining argument (its third), inverted or absent qualia, is the only one aimed at functionalism broadly, and it is explicitly prima facie. | Active |
| THEORY-472 v3 | A speaker who chooses words to minimise the information lost about a single intended referent, with words’ literal meanings uniform over their extensions, picks each true word with probability inversely proportional to a power of its extension, so the size principle follows from informative communication; in one betting experiment, learners who knew the referent bet on a novel word’s meaning in line with the inversion of that speaker (r = .93 on condition means), and in one free-description study speakers’ word use followed it only weakly (r = .19) | Frank, Goodman, Lai and Tenenbaum (2009), LIT-824, read in full in NOTE-627. The derivation (utility −D_KL from intended to literal meaning gives P(w) ∝ |w|^(−α) for a point referent) is a proof under its assumptions. Learners’ bets track the parameter-free inversion at r = .93 on condition means (700 web participants); speakers’ tag-word use in free descriptions correlates at r = .19, .51 without colour terms and .02 for them. In these displays the informative-speaker learner and a plain size-principle learner coincide by construction, so the fit does not show that learners reason about the speaker. | Active |
| THEORY-473 | Scaled down to one organism, Hutchinson’s niche, defined as the conditions that give that individual an expected lifetime reproductive success of at least one, is observed only as a point; the rest of it is counterfactual, reached by translocation in only a few dimensions and otherwise inferred from other individuals, so in practice it is the niche of a phenotype class, and its authors call it mostly metaphorical | Takola & Schielzeth (2022), LIT-127, read in full in NOTE-170. The working definition (p. 5) gives the individualized niche an absolute-fitness boundary, expected LRS ≥ 1, and splits it into realized, potential, time-slice, prospective and trajectory-based niches. That the realized niche is a point and the potential niche unobservable follows from the definitions. The paper concedes there is “no empirical solution” at the individual level (p. 15), and its fix, marginalizing fitness functions across individuals, is schematic. It is a framework for structuring research, by its authors’ own account, not a measurement. | Active |
| THEORY-474 | Spekkens’ toy bit theory, restricted to maximal knowledge and post-selected measurements, has a universal, sound and complete ZX-style graphical calculus whose phase-free rules and symplectic check-matrix conditions are exactly those of pure qubit stabilizer theory; the two calculi differ in the phase group, the Klein four-group against Z₄ | Backens & Duman (2014), LIT-054, read in full in NOTE-066. A red–green spider calculus interpreted in the category of relations is universal and sound, and complete by Backens’ stabilizer route. A binary matrix is a valid toy state iff SᵀJS = 0, the stabilizer condition (Lemma 3). The phase-free rules coincide with stabilizer ZX. That the phase group is the only categorical difference is cited, not shown, and completeness leans on analogy for several steps. The paper does no ψ-epistemic analysis and says nothing about which operational difference the phase group carries. | Active |
| THEORY-475 | In simulations from the drift-diffusion model itself, with 12 subjects and 20 to 150 trials each, hierarchical Bayesian estimation recovers every DDM parameter with less error than per-subject maximum likelihood, χ²-quantile fitting or non-hierarchical Bayes, most of all at few trials; whether the gain survives misspecification, and how much of the power gain is the hierarchy’s, is not shown | Wiecki, Sofer & Frank (2013), LIT-563, read in NOTE-466. Experiment 1 gives the lowest trimmed recovery error for HB on every parameter, and HB beat ML on the same data sets in every condition. Experiments 2–3 report more power to detect drift differences and trial-wise covariate effects, but HB was judged by a posterior-interval test and the others by t-tests, and the clean comparison was omitted. All data were generated from DDMs, with sz = st = 0. It is the standard partial-pooling result shown for one model family, not a test of the DDM. | Active |
| THEORY-476 | If continuant persons are maximal aggregates of person-stages interrelated by the psychological relation R, then the relation of belonging to one person is R itself, so Parfit’s premises do not show that identity is not what matters; the price is that persons overlap in fission and are counted by a relation weaker than identity | Lewis (1976), LIT-446, read in NOTE-373. Shown: that identity being one-one and all-or-nothing, and what matters branching and coming in degrees, do not entail that identity is not what matters, once stages and continuants are told apart; and that under supervaluation degrees of I-relatedness equal degrees of R-relatedness. Stipulated: that persons are the maximal R-interrelated aggregates. Conceded as costly: counting persons by tensed identity, which “is not a kind of identity”. | Proposed |
| THEORY-477 | None of the ten morphosyntactic criteria linguists use to identify words is necessary and sufficient for the orthographic word across languages, and the test batteries that combine them pick criteria opportunistically, so no cross-linguistically valid definition of the word is yet available | Haspelmath (2011), LIT-063, read in full in NOTE-073. Each of ten criteria (pauses, free occurrence, mobility, uninterruptibility, non-selectivity, non-coordinatability, anaphoric islandhood, nonextractability, morphophonological idiosyncrasy, biuniqueness) fails as necessary and sufficient against cross-linguistic counterexamples, and nine published batteries use no common set (Table 1). The target is orthographic practice by design. It does not say that words cannot be defined within one language, that sub-word units are privileged, or that morphology and syntax are shown to be one domain; whether units cluster on a boundness scale is open. | Active |
| THEORY-478 v2 | If the diffusion densities’ Hellinger distances obey a Hölder bound with exponent θ in d_T / t^(1/β) and are bounded below once d_T exceeds a multiple of t^(1/β), then for 0 < α < θ/β summing scale-weighted hyperbolic distances between diffusion densities over dyadic times gives a distance two-sided equivalent, up to constants, to min{1, d_T^(αβ)} for pairs above the finest scale: it keeps the tree’s neighbourhoods and not its global distances; whether a tree’s heat kernel, or sampled data, meets the bounds, and with which θ, is not shown | Lin, Coifman, Mishne & Talmon (2023), LIT-870, read in NOTE-675. The hyperbolic diffusion distance is equivalent to min{1, d_T^(2α)} for 0 < α < 1/2 (Proposition C.4), under heat-kernel bounds on the tree that are cited rather than proved; one Hölder step holds only for d_T ≥ 1, and repaired, the reader finds the admissible range halves. Pairs beyond a radius are only known to be far, which matches the method’s best mean average precision and its higher distortion than hyperbolic MDS on five graph benchmarks. A Euclidean distance on the same multiscale features does far worse. | Active |
| THEORY-479 | Shannon’s chain rule is the 1-cocycle equation of a cohomology of finite probability spaces whose action is averaged conditioning, and on connected, sufficiently rich structures of partitions every measurable 1-cocycle is a constant multiple of Shannon entropy, with no symmetry or continuity axiom assumed; in the unitary-invariant quantum version the first cohomology vanishes and von Neumann entropy is the 0-cochain whose coboundary is minus Shannon entropy | Baudot & Bennequin (2015), LIT-053, read in NOTE-088. Theorems 1 and 3 are proved for finite spaces, through the Tverberg–Kendall–Lee result on measurable solutions of the fundamental equation of information. The hypotheses are stated three different ways in the paper; Theorem 1’s is operative. The higher mutual informations appear as coboundaries, and Theorems B, D and F and the synergy reading are sketched or deferred to companion papers, so they are not part of this account. | Active |
| THEORY-480 v2 | Where a general-search monopoly was kept by exclusive distribution deals, the court in United States v. Google treated the user-interaction data that scale produced as a fruit of the violation and ordered the raw data and index metadata shared with qualified competitors, but not the engineered signals and models built from them, as a behavioural remedy while rejecting divestiture; that the sharing will let rivals compete is the court’s expectation, not a finding | Mehta (2025), LIT-006, the remedies opinion, read in full in NOTE-004. The court finds that exclusive distribution produced a scale advantage (9× the queries of all rivals; 93% of unique phrases seen only by Google), calls it a fruit of the violation, and remedies it with raw data and syndication rather than with divestiture, on a sliding scale of causal connection. Whether the shared data will let rivals compete is untested; the parameters that decide it were left to a Technical Committee. The opinion also finds no proof that search scale gives Google’s GenAI a quality edge (op. p. 156), which is an absence of proof, not a finding that there is none. | Active |
| THEORY-481 v4 | Under gradient flow averaged over tasks and data, a linear-attention layer trained on in-context regression learns as a two-layer linear network from an aligned start does: when tasks share the input covariance’s eigenbasis and the weights start and stay aligned with it, then in the long-context limit each input mode is learned on its own logistic curve whose timescale falls with the square of its variance, so learning is staged by the input spectrum, and the layer converges to the estimator preconditioned by the inverse input covariance; at finite context length the modes decouple exactly only when inputs are isotropic and the modes start equal, and otherwise couple at order 1/N | Mainali & Teixeira (2025), LIT-859, read in NOTE-658. The prediction of one linear-attention layer reduces to p₂ W Σ̂_x q₁ x_q, a product of two learned factors, so averaged gradient flow decouples into modes with τ_α dp_α/dt = q_α(1 − p_α q_α s^∞_α) and τ_α = (ηP s_α²)⁻¹, logistic from a balanced start. The fixed point is ŷ = W Σ̂_x Σ_x⁻¹ x_q as N → ∞. The paper’s finite-N form, the one Ahn et al. and Zhang, Frei & Bartlett found, holds at finite N only for isotropic inputs with equal modes. The trajectory is new. The decoupling into independent modes is exact as N → ∞. At finite N it holds only for isotropic inputs with equal modes: the paper commutes the non-diagonal empirical covariance at (A71) and (A73), and the correct Wishart moment couples the modes at order 1/N. Alignment of the weights with the data’s eigenbasis is assumed throughout, the null blocks vanish only in expectation over tasks, and the transfer to non-linear transformers is timing coincidences. | Active |
| THEORY-482 | For a closed quantum system that starts thermal and is measured projectively in energy before and after a unitary drive, the two-point-measurement work obeys the Jarzynski equality and the Tasaki–Crooks relation in exactly the classical form, because those energy measurements erase the coherences in which a quantum difference could appear | Vinjanampathy & Anders (2015/16), LIT-010, read in full in NOTE-011, which reproduces the derivation (Eqs. 24–30). With W_{m,n} = E_m^(τ) − E_n^(0), a thermal start and closed unitary evolution, ⟨e^{−βW}⟩ = e^{−βΔF} follows from Σ_n p_{m|n} = 1 (Eq. 29), identical in form to the classical relation. The identity is exact under its conditions. Its classicality is bought by the definition of work: two projective energy measurements destroy coherences, which is why the definition is contested. It says nothing about work defined without them. | Active |
| THEORY-483 | Whether a person joins a fascist movement in a showdown is decided by inner disposition, whether she is secure and has a standard of her own that tells her what she likes and does not, and not by race, nationality, creed or class; humiliation, fear, spoilt entitlement and measuring worth by success make a person susceptible | Thompson (1941), LIT-055, a Harper’s essay read in NOTE-056. A typology argued through vignettes of an imagined party, from a reporter who had watched Nazism rise in Germany, Austria and France. No case is verifiable, the typology is applied inconsistently (two “born Nazis”; one man both never and qualifiedly a Nazi), and its denial that class is the criterion sits badly with sketches that are mostly about class. It is filed for what Thompson argued, and the empirical literature that tested such typologies is not yet read. | Proposed |
| THEORY-484 | The brain implements hierarchical reinforcement learning with options: dorsolateral prefrontal cortex represents which option is active, dorsolateral striatum holds option-specific policies, orbitofrontal cortex holds option-specific values, and dopamine carries option-level prediction errors at subtask boundaries | Botvinick, Niv and Barto (2009), LIT-581, read in NOTE-451. Four proposed extensions of the actor-critic mapping, each matched to existing correlational findings, and predictions the authors say “call for further experimental scrutiny”. The evidence for prefrontal coding of subtask segments is “only indirect”. The mapping assumes pseudo-reward; other frameworks (HAM, MAXQ) would predict differently. | Proposed |
| THEORY-485 | Wave-function realism falsifies causal closure restricted to spacetime but is compatible with closure relative to fundamental physics, so quantum ontology opens no causal gap for non-physical causes; what it forces on the physicalist is a criterion of the physical and a bridge from dynamical to causal completeness | Poltorak (2026), LIT-164, an unrefereed preprint read in full in NOTE-112. “Every physical effect has a sufficient physical cause” has two tacit parameters, a domain and a completeness relation. With the domain set to spacetime the principle fails under wave-function realism; with it set to the ontology of a complete fundamental theory it survives. The move to a breach needs a premise that wave-function realists deny. The conclusions are modest and close to analytic once the terms are defined. The target is conceded to be a picture, not a published argument, and the dynamical-to-causal bridge is asserted, not argued. | Proposed |
| THEORY-486 | For exact Betti Lagrangians in the cotangent bundle of a punctured surface, a finite creative spectral network exists, a point lies on its active walls exactly when a pseudo-holomorphic strip survives the adiabatic limit, and the Family Floer functor equals Gaiotto–Moore–Neitzke non-abelianization there | Casals & Nho (2025), LIT-017, an unrefereed v1 preprint read in full in NOTE-022 by a reader who is not a Floer theorist. Theorems 1–3 are stated for any rank and for positive-braid asymptotics. The proofs cover exact Betti Lagrangians with finite creative networks; the meromorphic case adds hypotheses in prose, and the Family Floer functor is not built there. The analytic core is taken by citation from Ekholm 2007, which the authors patch, and from the second author’s own preprint. Theorem 5, on networks from Demazure weaves, has no written proof and is not part of this account. | Proposed |
| THEORY-487 | Social ontology asks two separable questions about a social category: what grounds a fact of that kind, the conditions something must meet, and what anchors those conditions, the facts that put them in place; theories of the field, such as convention, collective acceptance and practice, answer the second, and a theory can be individualist about one and not the other | Epstein (2018; rev. 2024), the SEP entry Social Ontology, LIT-487, read in NOTE-393 with the author’s précis of The Ant Trap (LIT-478, otherwise unread). A survey organised by its author’s own distinction, likened to semantics and metasemantics. It rests on a survey that reports the dissents (Hawley, Schaffer, Haslanger) in a sentence each and argues the distinction by example. Whether anchoring is a relation distinct from grounding is reported as the author’s view and as disputed. | Proposed |
| THEORY-488 v2 | Clark (2020), synthesising open writing by Russian military authors of 2015 to 2020, chiefly Chekinov and Bogdanov, Bartosh and Kiselev, with no stated rule for choosing sources, reports that they use “hybrid war” for a category of war marked off by its objective, reshaping a target state’s governance, geostrategic orientation and worldview, in which every action up to conventional military force is subordinate to an information campaign, and not, as he says Western usage does, for a set of means below the threshold of armed conflict | Clark (2020), LIT-023, an ISW report read in NOTE-012. A synthesis of open Russian military journals, official press and speeches, 2015–2020, with no stated method for choosing sources; the definition is the author’s synthesis of several writers, not a doctrinal text. The reading rates the definition moderate, the claim that it is institutional weak to moderate, and the US policy recommendations advocacy. Written before the 2022 invasion. | Active |
| THEORY-489 | Chains of human function learners, each trained on the previous learner’s responses, forget their starting function and in 28 of 32 families converge within a few generations to a positive linear function, the bias earlier studies report, whatever function trained the first learner; this is convergence to the learners’ favoured function, not shown to be convergence to their prior | Kalish, Griffiths & Lewandowsky (2007), LIT-820, read in NOTE-616. 288 participants in 32 nine-generation chains, four starting conditions. 28 families converged to a positive linear function; 3 converged to the negative linear one and 1 had not converged. The bias was taken from earlier studies, not measured on these learners, and stationarity was not established. It supports the claim that human transmission chains settle on what learners favour in this task, not that they reach the Bayesian prior, and it cannot tell sampling learners from MAP learners. | Active |
| THEORY-490 v2 | What a chat agent’s ‘I’ refers to is fixed by the context of use, not by the system: the agent role-plays characters that carry the self-conception the corpus and the conversation give them, and its uses of ‘I’ can pick out the model, present in many simultaneous instances, or the single conversation, none of them the self by nature | Shanahan (2025), LIT-466, read in NOTE-376, with Shanahan, McDonell and Reynolds (2023), LIT-460, read for the self in NOTE-370. The candidate sites of an LLM’s “I”, and the fact that a conversation-bound self is literally a transcript and a program, are solid. That both the model and the conversation are legitimate referents rests on two invented usages. It does not say that there is “no-one at home” or that no candidate is a self, which the papers assert without a criterion, and its subject is a 2024-vintage chat agent without tools or memory across conversations. | Proposed |
| THEORY-491 | Of the five standard arguments that randomisation gives a clinical trial special evidential weight, only the selection-bias argument is sound, and it supports only taking allocation out of the experimenters’ hands; given balance on plausible confounders, a placebo or active control and blinding, randomisation is argued to add nothing, since balance on unknown confounders is not even probable in the one division a trial makes | Worrall (2007), LIT-175, read in NOTE-126. The case against the unknown-confounders argument is conceptual: frequentist balance is a long-run claim about repeated divisions, and a trial divides once. It does not show that randomised designs are no more reliable in practice than matched ones, and the meta-research cited is mixed. The selection-bias argument is conceded as “cast-iron”, so the account does not say randomisation is worthless. Haphazard allocation is asserted to serve as well, without discussing whether such rules are predictable. | Proposed |
| THEORY-492 | Life was forced into existence by geochemistry: core metabolism, rooted in the reductive citric-acid cycle, formed as a channel relieving the free-energy stresses abiotic processes keep building, as lightning relieves a charge separation, so its early steps would recur on any similar planet and selection on metabolism came before replication | Morowitz & Smith (2006 working paper; Complexity 2007), LIT-528, read in NOTE-425. An essay with no calculation, which says itself that the thesis “has not been quantitatively demonstrated”. Its evidence is the structure of present-day core metabolism, read back into its origin. Its framework is Jaynesian entropy maximization over states that include currents, and it rejects entropy-production principles. The reading judged that no THEORY was indicated; this one is filed as Proposed, a conjecture with a stated research programme. | Proposed |
| THEORY-493 | From core mereology, classical extensional mereology (GEM) is reached by exactly three pairings of a decomposition principle with an unrestricted-sum principle: Supplementation with Sum2, Strong Supplementation with Sum3, and Complementation with Sum1; Supplementation with Sum3, the pairing given by Simons (1987), does not yield it, because which definition of ‘sum’ is used decides which decomposition axiom is needed | Varzi, SEP “Mereology” (2003, revised June 2026), LIT-124, read in full in NOTE-163. A result the entry reports with citations (Hovda 2009; Cotnoir and Varzi 2019) and a countermodel (its Fig. 4; Pietruszczak 2000a, Pontow 2004), and which corrects Simons (1987), Casati and Varzi (1999) and the entry’s own 2003 edition. The record has not checked the proofs. It is stated for first-order theories with a single primitive P and infinitary principles as axiom schemas, and it is a fact about axiom systems: it does not say classical mereology is true of anything. | Active |
| THEORY-494 | Puritanical norms against harmless bodily pleasures are cooperative morality: people believe cooperation needs self-control, which indulgence erodes and discipline trains, and condemn indulgence as an indirect threat to cooperation | Fitouchi, André & Baumard (2021), LIT-101, read in NOTE-132. In the authors’ vignette studies (N > 1,100), perceived loss of self-control mediated all of the perceived effect of indulgence on cooperativeness. The rest is a review: disgust does not amplify condemnation once harm is controlled, and a society’s valuing of self-control predicts its hygiene norms better than pathogen threat. The account is agnostic about whether the norms work, excludes contamination purity by definition, and has shown that people hold the belief, not that the belief made the norms. | Proposed |
| THEORY-495 | The human sense of obligation is internalized pressure from a joint agent ‘we’ to do what ‘we’ expect of me; it appears around age three inside joint commitments, where children, unlike chimpanzees, protest, repair, take leave and share equally with a committed partner as they do not with others | Tomasello (2019), LIT-125, read in NOTE-185. A synthesis of developmental and comparative experiments, mostly from the author’s lab, on WEIRD children and chimpanzees; no new data. The behavioural contrasts between committed and side-by-side play are moderately supported. That they reflect felt obligation, rather than prosociality or learned scripts, is argued, not shown. It explains the sense of obligation, not what anyone is obliged to do, as the author concedes. | Proposed |
| THEORY-496 | In few-shot classification and multiple choice by language models up to 175B parameters, whether each demonstration’s label is correct contributes little to the gain over zero-shot, while the distribution of the inputs, the label space and the paired format carry most of it | Min et al. (2022), LIT-814, read in NOTE-607. With k = 16 demonstrations, labels drawn at random from the correct label set cost 0–5 points against gold labels (2.6 on classification, 1.7 on multiple choice on average) across twelve model–inference combinations and 26 datasets. Out-of-distribution inputs, random English words as labels, or breaking the input–label pairing each cost far more. The random labels always come from the right label set, gaps reach about 14 points on single datasets, and the authors’ reading that the models learn no new correspondence at test time is untested on tasks pretraining cannot have taught. | Active |
| THEORY-497 v3 | A macro feature can supervene on a system’s present state and still carry information about its future that no small set of parts carries, because supervenience is instantaneous and prediction runs across time; on the integrated-information-decomposition account a system can host such a feature of order k exactly when its dynamics carry k-th-order synergy about their own future, relative to a fixed partition into parts and a chosen redundancy function | Mediano et al. (2022), LIT-025, read in NOTE-010, a review of Rosas et al. (2020), which the record does not hold. A feature V_t is causally emergent of order k iff Un⁽ᵏ⁾(V_t; X_t′ | X_t) > 0, and a system has one iff Syn⁽ᵏ⁾(X_t; X_t′) > 0, split as downward causation plus causal decoupling. The review proves none of this and names no redundancy function. The quantities change with the partition, which the review calls intended, and they are predictive, not interventional, unless p(X′ | X) is a do()-distribution. | Proposed |
| THEORY-498 | A mathematical structure whose domains are aspects of experience and whose axioms hold there is not thereby a structure of experience, because that test passes incompatible topologies on one set and every rescaling of a metric without consulting experience; requiring, for each relation, an aspect that changes exactly when a variation of experience breaks the relation removes those automatic passes, and has so far been met only by relative similarity and a visual topology, each on an assumed premise | Kleiner & Ludwig (2023; Synthese 2024), LIT-143, read in full in NOTE-135. The negative result is shown by construction: any set of aspects carries both the discrete topology and a coarser one, and a metric d passes whenever every C·d does. The replacement criterion (MSC) ties each relation to an aspect that co-varies with it under every variation. Its two positive cases rest on assumed transitivity and on the subsumptive unity thesis. The published version gives no structure that fails (MSC); the argument that metric spaces fail is in arXiv v1 only, and was withdrawn. | Active |
| THEORY-499 v2 | The breakup of the Eulalia parent body beside the Jupiter 3:1 resonance, 785–965 Myr ago, can plausibly have supplied the cluster of large lunar craters dated near 800 Ma, but shown only for the most favourable of five model solutions, the one carried through, with an average largest lunar impactor too small for Copernicus, and with the cluster’s absolute date inherited from Copernicus alone | Bottke, Vokrouhlický, Dykhuis & Zellner (2026), LIT-009, read in full in NOTE-002. A chain of multiplied factors (family fit, J3:1 influx, WISE incompleteness, collisional loss, impact probabilities) gives, for Solution 5 only, about 7,000 D ≥ 2 km fragments into the resonance and a largest expected lunar impactor of “>3 km”. A Monte Carlo puts the seven ~800 Ma craters “generally” within 1σ. It is an existence argument, not an estimate: one factor is tuned by eye, only the most favourable solution is propagated, and the seven craters are dated by N(1) against one sample-dated crater. The Earth, Mars and Venus links are the authors’ own speculation. Active as a reading of the model (ADR-065); whether the shower happened is THEORY-1195, Proposed. | Active |
| THEORY-500 | Ventromedial prefrontal cortex stores links between kinds of situation and the body states they produced, and re-enacting those states when an option is imagined marks it good or bad, overtly as a feeling or covertly as a bias, pruning the options before reasoning weighs them; without the marks, choice under uncertainty fails despite intact knowledge and intellect | Damasio (1996), LIT-384, read in NOTE-332, the somatic marker hypothesis stated by its author; Bechara, Damasio, Tranel and Damasio (1997), LIT-383, read in NOTE-331, the experiment it is usually cited for. The robust result is a group difference: in the gambling task all 10 controls and none of 6 ventromedial patients developed anticipatory skin conductance responses. That controls chose well before they knew, and that the marker causes the choice, is not carried by the statistics. The mechanism is argued, not observed. | Proposed |
| THEORY-501 | In weekly waste collection where each point’s visit days are free and its bin capacity must cover the longest gap between visits, a genetic algorithm that searches visit schedules and derives bins from them builds routes about 6% cheaper than eight-hour Gurobi incumbents but buys about 20% more bin capacity, ending level on overall cost at its best of 30 runs and 4–6% worse on a typical run, on five 12-point instances where the incumbents’ own optimality gaps are 26–32% | González et al. (2025), LIT-008, read in NOTE-015. The comparison is against incumbents whose distance from optimum is unknown, on five 12-point random subsets of one real instance, one of which was also used to tune the GA. Best of 30 against the MILP: −0.08% overall; against the MIQP: +1.70%; the GA’s mean or median is +3.75% and +5.61%. The abstract’s “able to match the results of exact solvers” says less than it appears to. On 40–163 points there is no bound or baseline. | Active |
| THEORY-502 | Forman–Ricci curvature of a graph edge, taken with no cells above the edges, depends only on the weights of the edge, its two endpoints and the edges adjacent to it, and with unit weights reduces to 4 − deg(v₁) − deg(v₂); it is a local, closed-form degree-and-weight statistic that sees no triangles or cycles, unlike Ollivier’s curvature, which needs a transport problem per edge | Weber, Saucan & Jost (2016; J. Complex Networks 2017), LIT-020, read in full in NOTE-026, which checked the formulas against page renders. The formula (Eq. 11) is Forman’s (2003) Bochner–Weitzenböck curvature specialised to a 1-dimensional complex by dropping the parent terms; the unit-weight form is NOTE-026’s substitution, not stated in the paper. The paper’s applications (an EMD distance between curvature distributions, a Ricci flow for change detection, a Laplacian flow for denoising) are one-table or one-figure demonstrations, and several of its formulas carry sign and consistency slips, so it is cited here for the definition only. | Active |
| THEORY-503 | The nearest rank-r matrix to a real matrix in the least-squares norm keeps its r largest singular values and zeroes the rest; it is unique when the r-th and (r+1)-th singular values differ, its squared error is the sum of the dropped squares, and the singular-vector factors that build it are not unique | Eckart & Young (1936), LIT-330, read in full in NOTE-301, which checked the error bound. The argument is first-order stationarity on the orthogonal group plus two cited theorems (the SVD and a simultaneous-SVD criterion), and assumes a minimiser exists. Only the Frobenius norm and real matrices are covered. Uniqueness is of the approximating matrix, under a spectral gap, never of the factors; the paper’s last section argues the canonic components cannot be read straightforwardly as psychological factors. | Active |
| THEORY-504 v2 | In the Gemma Scope sparse autoencoders on Gemma 2, the two fidelity measures disagree by site: residual-stream autoencoders cost more next-token loss than MLP or attention ones at comparable fraction of variance unexplained, and base-model autoencoders transfer to the instruction-tuned model by loss more than by variance explained | Lieberum et al. (2024), LIT-611, read in NOTE-482. Across every layer and sublayer of Gemma 2 2B and 9B, JumpReLU autoencoders on the residual stream raise the language model’s loss more, when spliced in, than MLP and attention autoencoders whose FVU is about the same; and autoencoders trained on the base model lose little loss on instruction-tuned rollouts while showing a larger FVU gap. The authors’ explanations (the residual stream is the bottleneck; fine-tuning re-weights old features) are conjectures, and the authors say no agreed metric of autoencoder quality exists. | Active |
| THEORY-505 | Questionnaire items written for morality-as-cooperation’s seven domains form seven factors when rated for relevance to moral decisions, in the UK, the US and Turkey, but not when rated as agreement with moral statements, and the two formats cannot be pooled into seven domains | Curry, Jones Chesters & Van Lissa (2019), LIT-496, read in NOTE-412, and the independent Turkish validation by Yilmaz, Harma & Doğruyol (2021), LIT-513 (NOTE-397). Relevance items fit seven factors in all three samples (CFI .98 UK, .95 Turkey). Judgement items do not (CFI .87, .83), and a seven-domain model of both fails (CFI .73, .75). The items were written from the theory and selected for fit within each domain, several subscales correlate above .8, and no item is non-cooperative. This is evidence about the instrument’s structure, not about what morality contains. | Active |
| THEORY-506 | Every well-developed theory of how mind fits into the cosmos is bizarre, contrary to what most people confidently believe, and none is epistemically compelling, because common sense about the metaphysics of mind is incoherent; so no coarse position, materialism included, deserves credence much above 50% | Schwitzgebel (2024), LIT-216, read in full from the June 2022 final manuscript in NOTE-188; the published body text was not reached. Chapter 3’s Universal Bizarreness and Universal Dubiety, with the other chapters as case studies. Bizarreness is an abductive generalization over the theories actually developed, with a standing challenge to find a counterexample, not a result about all possible theories. Dubiety rests on expert disagreement, the lack of any method and cosmological uncertainty, and the 50% figure is the author’s judgment. The author’s own credences lean materialist, at about 55%. | Proposed |
| THEORY-507 | Any system with the same fine-grained functional organisation as a conscious system has qualitatively the same experiences, with natural though not metaphysical necessity, because otherwise a neuron-by-neuron replacement would yield either a rational subject systematically wrong about its fading experience or experience that flips with a switch nobody could notice; the principle covers only isomorphs, so it says nothing about systems merely similar in kind to a conscious one | Chalmers (1995), LIT-392, read in full in NOTE-347, with the one-page sketch in “Facing Up”, LIT-406 (NOTE-336). A plausibility argument by the author’s own account: the fading- and dancing-qualia conditionals are strong given the replacement series; their rejection rests on a premise about self-knowledge drawn from familiar cases. It extends to a population of people implementing a person’s neurons, so it rules out absolute anti-nesting for isomorphs. It does not reach any system that is not an isomorph of something conscious, which includes every actual AI system and every group. | Proposed |
| THEORY-508 | The Belousov–Zhabotinsky oscillation is a relaxation cycle in which autocatalytic production of HBrO₂ oxidizes the catalyst until bromide, released as the oxidized catalyst is reduced by bromomalonic acid, switches the autocatalysis off; a closed batch oscillates only as a transient of up to several thousand cycles on its way to equilibrium, and only a continuous-flow reactor sustains it indefinitely | Zhabotinsky (2007), LIT-531, the Scholarpedia review by one of the reaction’s eponyms, read in full in NOTE-414. The mechanism is supported by the primary kinetics and by phase-resetting with injected Br⁻, Ag⁺ and Ce⁴⁺. The closed/open distinction matters for any use of BZ as a dissipative structure: a closed batch is a long transient, and only a fed reactor holds it away from equilibrium. The Oregonator models oscillation and excitability qualitatively, not quantitatively. The “several thousand cycles” figure is uncited, and the primary papers were not read. | Active |
| THEORY-509 | Under genericity conditions, two dense or top-k (k ≥ 2) mixture-of-experts layers compute the same function only if they differ by a permutation of the experts with their gates and a common translation of the gate weights, and the translation leaves every interpolation barrier unchanged, so expert order is the only gate symmetry alignment must undo | Tran, Trinh, Bui & Nguyen (2025), LIT-670, read in NOTE-513. Softmax is invariant to a common shift of scores and the sum to the order of terms, so G(n) = ℝ^d × ℝ × S_n preserves the layer; Theorems 4.1–4.2 show that generically it is all of the gate’s symmetry, for dense gating and for top-k with k ≥ 2 (top-1 has an extra scaling). Aligning expert order and then each expert’s hidden units gives barriers of 0.0044–0.0066 between GPT-2 MoE layers fine-tuned from different seeds, against 0.14–0.86 without the order step. Every experiment shares and freezes the backbone around the inserted layer, so it is not evidence about independently trained MoE models. | Active |
| THEORY-510 | How much of an ImageNet image a crop must keep for its label to survive varies widely by class, with architectures agreeing on which classes are fragile, and strengthening random crop raises mean accuracy while some classes lose 20 points or more; how many classes lose is not established | Balestriero, Bottou & LeCun (2022), LIT-234, read in NOTE-845. Six pretrained models on cropped test images keep some classes recognisable at an 8% crop and lose others below about 50%, and agree on which. Over 20 ResNet-50 runs, moving the crop lower bound from 100% to 8% raises mean accuracy from about 70% to 76% while “academic gown” falls from about 62% to 40%. The classes shown are hand-picked; the per-class test rejects for 4.4% of classes at the 5% level, uncorrected for 1,000 tests, which alone is not more than chance; and evaluation-set noise is not counted. Theorem 1 does not reach which classes pay. | Proposed |
| THEORY-511 | Illocutionary acts that are not essentially conventional, such as warning, entreating and objecting, are individuated by a wholly overt, audience-directed intention, Grice’s three intentions with a fourth that the audience recognise the second, and are performed when that intention is understood; acts such as verdicts and umpires’ calls exist only within rule-governed procedures and fall outside the scheme | Strawson (1964), LIT-1043, read in full in NOTE-736, amending Grice (1957), LIT-1042. Against Austin, some illocutions need no convention beyond the linguistic; their force is an overt intention meant to be understood, and uptake is the audience’s recognition of it, an aim rather than an achievement. Orders fit “with some strain”; verdicts, umpires’ calls and marriages do not fit at all. The scheme predicts no non-institutional case in which the overt intention is fixed and the act changes, which gives QUESTION-073 a definite rival to test. The amended analysis is offered as necessary, not sufficient. | Proposed |
| THEORY-512 | The extended-mind thesis worth disputing is that external entities partly constitute a subject’s mental states in virtue of the subject’s sensorimotor interaction with them; so stated it can reach standing belief but not consciousness, if consciousness needs information directly available for global control, since perception makes availability indirect | Chalmers (2019), LIT-415, read in NOTE-356, and his foreword to Clark’s book (2008), LIT-421, read in NOTE-369. The 1998 thesis is satisfied by wired-in “extended circuits” that its critics accept, so the controversial thesis is constitution through perception and action. The perception-action boundary is then the strongest objection, met by revisionism, not refuted. Consciousness does not extend this way, on an imported criterion (direct availability, “not mediated by other mental states”) and on the absence of any working twin case. Both halves are proposals defended against a few cases; the criterion is the author’s earlier correlate of consciousness, not an argument made here. | Proposed |
| THEORY-513 | Observational entropy taken relative to a maximum-entropy prior τ, S(τ) − D_M(ρ‖τ), lies between S(ρ) and S(τ) for states meeting the prior’s constraint, is finite and continuous whenever S(τ) is, and reduces to about two dozen textbook entropies by choice of measurement and prior; its second laws are bounds on the time-averaged state’s divergence from the prior, proved small only under sufficient conditions (nondegenerate energy gaps for equilibration, the eigenstate thermalization hypothesis for fit to the prior) | Schindler, Strasberg, Galke, Winter & Jabbour (2025), LIT-082, read in full in NOTE-043, with Proofs 1, 2, 7, 10 and 11 checked line by line. The bounds, the special cases and the decomposition are proved. The central target, a small divergence of the time-averaged state from the prior, is proved for no concrete system; in the paper’s own examples “in none of those cases was the smallness proved here analytically” (p. 12). Unpublished as of the reading. | Active |
| THEORY-514 | Self-maintenance through closure of constraints does not single out organisms, since colonies, holobionts, symbioses and ecosystems meet it too, so a persister criterion applied at whatever level meets it turns organisms into parts; what is proposed to mark organisms is that they can also induce, control and come through phases of destabilised organisation and reach a new closure regime, though that only organisms can do so is asserted | Baedke (2025), LIT-167, read in full in NOTE-148. The negative half, that persister criteria are too permissive, is argued from the literature: closure has been applied to symbioses, ecosystems and eusocial colonies, and Mossio (2024) concedes that “organized systems are not necessarily organisms”. The positive half, the overcomer, is drawn “with rough brushstrokes” (p. 51) from three cases, two of which are lineage-level evolution or colony-triggered plasticity, and its uniqueness to organisms is asserted, with the one contrast (colony against ant) presupposing its verdict. Proposed. | Proposed |
| THEORY-515 | Sampling a posterior p(x|y) when only joint samples (X, Y) can be drawn is solved by a Schrödinger bridge on the joint space, with y held fixed along the path, between the joint distribution and any reference sharing its y-marginal; the bridge averages the per-observation bridges, its first iterative-proportional-fitting step is the conditional score-based model, and the error of later steps at the data end falls as 1/n times the reference’s distance from the bridge | Shi, De Bortoli, Deligiannidis & Doucet (2022), LIT-776, read in NOTE-589. Propositions 1–3 are proofs, read for structure and not checked line by line. The empirical gains over the conditional score model hold at equal, small step counts on most but not all image metrics, and in Lorenz-63 filtering at 20 steps. That a long noising horizon is not what makes conditional diffusion correct is NOTE-589’s interpretation, not something the paper tests. | Active |
| THEORY-516 | For any presheaf of propositions over a small category of contexts, a sieve-valued valuation satisfies the generalized functional-composition condition exactly when it is a subobject of that presheaf, and the construction runs unchanged in classical physics, where every microstate gives a global section yet truth values are still non-Boolean sieves; so the logic of the truth values is fixed by the base category, not by whether a presheaf has global sections | Butterfield & Isham (1998), LIT-381, read in full in NOTE-329: Theorem 4.1 proves that generalized FUNC is exactly naturality of ν : G → Ω, for any presheaf G of posets on any small category. In classical physics the value presheaf has a global section per microstate (3.6–3.7), yet the macrostate and microstate valuations are sieve-valued, and NOTE-329 shows excluded middle failing at a microstate. Isham & Butterfield (1999), LIT-389 (NOTE-334), adds that Ω is unique for a given topos and that a base with one arrow between any two objects gives two-valued logic. The choice of base, and so of the logic, remains free. | Active |
| THEORY-517 | Life raises the Earth’s entropy production, chiefly by increasing the absorption of sunlight, and if the planet is held at maximum entropy production, the negative feedbacks of that state would give the homeostasis the Gaia hypothesis postulates | Kleidon (2009), LIT-519, read in NOTE-423. The Earth’s entropy budget is dominated by the absorption of sunlight, and model studies, mostly the author’s, find that biotic activity raises it. The step to Gaia is explicitly conditional on MEP, which the same review says is not established, and its feedback argument is a schematic figure. It treats life as the most effective of the Earth’s dissipative processes, and gives no criterion separating a living dissipator from a convection cell. | Proposed |
| THEORY-518 | If a word’s meaning in a distributional model is read differentially, as its relations to its nearest neighbours rather than its coordinates, then adding text moves every similarity value slightly but leaves the neighbourhoods of frequent, consistently used words intact and shifts those of rare words that the new text uses heavily, so the instability that holism implies is local and graded rather than total | Grindrod, Porter and Hansen (2024), LIT-208, read in full in NOTE-158. The conceptual reply to the instability objection is argued; the empirical half is four hand-picked words in two before-and-after demonstrations (a count model on Stein plus a Hemingway story; Word2vec on Wikipedia plus the SEP), top-10 lists, one run each, no metric. The abstract’s proportionality of resistance to frequency is not measured, the criterion used (a preserved neighbour list) is not the one defined (relative distances), and static embeddings only are tested. | Proposed |
| THEORY-519 | Supervised learners compose only once each carries a request function that passes a corrected input upstream; with it they form a symmetric monoidal category, and for a fixed step size and an error whose derivative in its first argument is invertible, gradient descent with backpropagation is a faithful strong symmetric monoidal functor into it from differentiable parametrised functions | Fong, Spivak & Tuyéras (2017; LICS 2019), LIT-827, read in full in NOTE-625, which followed the chain-rule proof of Theorem A.1 line by line. Learners (P, I, U, r) form Learn (Prop. II.4); Theorem III.2 makes gradient descent with backpropagation a functor Para → Learn. Covered: fixed step size, one datum per update, deterministic updates, and errors with invertible ∂e/∂x, which excludes cross-entropy at 0 and 1. That learners cannot compose without a request is argued, not proved. Learn says how learners compose, not whether they learn. | Active |
| THEORY-520 | When coordination between two autonomous agents and the continuation of their encounter shape each other, the interaction gains an autonomy of its own, a precarious self-sustaining organization that lasts only while both agents stay autonomous; coordinating movement then coordinates sense-making, so some social understanding, such as recognising a partner, is a property of the interaction’s dynamics and not of either individual | De Jaegher and Di Paolo (2007), LIT-571, read in NOTE-456. A conceptual account built on coordination dynamics, with illustrative evidence: the corridor, charades, mother–infant timing and the perceptual-crossing experiments of Auvray et al., reported, not new. NOTE-456 declined a THEORY because the source carries no claim beyond its definition. The claim with some support is the perceptual-crossing one; the autonomy of the interaction is a definition, and the implications are called “speculative at this stage” by the authors. | Proposed |
| THEORY-521 | In the thermodynamic limit, with examples and capacity growing together at fixed load, generalization error can jump discontinuously with the load when the entropy of hypotheses just above the best error vanishes faster than the training-error energy grows: a spherical perceptron’s error falls smoothly as 1/α, an Ising perceptron’s drops to zero at a critical load | Martin & Mahoney (2017), LIT-672, read in NOTE-542, restating Seung, Sompolinsky & Tishby (1992) and Haussler, Kearns, Seung & Tishby (1996), which the record does not hold. Generalization is set by maximizing s(ε) − α ln(1/(1 − ε)). For weights on a sphere s(ε) ~ ln ε and ε ~ 1/α; for ±1 weights s(ε) ~ −(π²/2)ε² ln ε, the first-order condition has no solution past a critical load, and the error drops to zero. Uniform bounds that see a class only through its size or VC dimension are smooth and blind to this. That deep networks have such a phase diagram is the authors’ conjecture, and their mapping of label noise to load and early stopping to temperature is an analogy. | Proposed |
| THEORY-522 | Open text-to-image diffusion models of 2022–2023 render a single named object almost always but fail most on relative position and next on attribute binding, by human rating and by detector checks alike; scaling the image model or continuing pretraining does not fix position, and interactions are rated near ceiling only by rubrics that ask whether an action is depicted | GenEval (Ghosh, Hajishirzi & Schmidt 2023, LIT-782, NOTE-593) and T2I-CompBench with its journal extension (Huang et al. 2023 and 2025, LIT-783 and LIT-798, NOTE-592 and NOTE-610), two independent benchmarks that do not cite each other. GenEval: single object 0.97–0.98 for every diffusion model, position at most 0.15, binding at most 0.35. Human ratings in T2I-CompBench: 2D spatial 0.31–0.46, shape binding 0.51–0.70, interactions 0.81–0.99. Human ratings cover only six 2023-era models; the 2024–25 generation is ranked by automatic judges validated on the older ones, so the ordering is not established for it. | Active |
| THEORY-523 | IIT 4.0’s measure of integrated information is undefined for any system that has a non-Markovian graining, which brains are said to have under the grainings in use, and it has never been computed for a real physical system; so empirical measures such as PCI are proxies for it, not approximations, and their success is evidence for IIT’s intuitions about integration, not for Φ | Barrett, Milinkovic, Mediano, Rosas, Bor, Barnett & Seth (2026), LIT-185, read in full in NOTE-122. A position paper by sympathetic insiders, with no new formal result. The ill-definedness is restated from Barrett & Mediano (2019), which the record does not hold. That brains are non-Markovian under typical grainings rests on one 1998 citation about ion-channel currents. The proxy point follows from a definition: an approximation needs a well-defined target and an error bound. The paper’s defences of IIT (the multi-dimensional measure, the “proto-consciousness” panpsychism) are revisions of the theory, not readings of it. | Proposed |
| THEORY-524 | On cyclic measurement scenarios, where the contexts’ overlaps form one chordless N-cycle, the ℤ/2 Čech obstruction computed on the (N−1)-th iterated joint model is exact for logical and strong contextuality, the bound N − 1 being tight; beyond cycles no such result is established, the published extension is false on its own example, and the completeness conjecture fails on a Kochen–Specker cover that is never detected at any level | Carù (2018), LIT-280, read in NOTE-253, and the same result republished as Thm IV.32 of Carù’s 2019 thesis, LIT-281, read in NOTE-254. The cyclic theorem is proved and was confirmed on Hardy, on the (2,2,4) counterexample and on 659 random contextual cycle models. The failures beyond cycles (Prop 8.2 / IV.34, the §8 cover, Conjecture 9.1 / IV.41) are the readers’ computations and a lifting lemma, not the author’s. The joint models grow exponentially; nothing analyses the cost. | Active |
| THEORY-525 | In fan–celebrity parasocial relationships the celebrity mostly directs fans’ identities and the fans mostly interpret the celebrity’s, so a mass audience that refuses uptake of a legitimately presented change of persona holds one person’s identity fixed, which is a failure of recognition respect that restricts the celebrity’s agency | Archer & Robb (2025), LIT-172, read in NOTE-186. Three structural asymmetries (attention, communication, epistemic) yield an identity asymmetry, after Cocking & Kennett’s directive and interpretive influence; on Darwall’s and Lindemann’s accounts, refusing uptake of a presented self is a wrong. Informal argument from one main case (Taylor Swift, 2018). The duties derived are fans’ only, though the abstract promises celebrities’ too. It needs a person on the far side, so it does not carry over to AI companions without an argument about their moral status. | Proposed |
| THEORY-526 | The Čech cohomology obstruction of a support section is a sound but incomplete witness of contextuality: it vanishes exactly when the section lies in a compatible family of integer combinations of support sections, so it is non-zero on every section of every All-vs-Nothing model, over any coefficient ring, on a connected cover, yet it misses the Hardy model entirely, part of a strongly contextual Kochen–Specker cover, and every section of a strongly contextual model on the fully symmetric (2,2,4) Bell cover | Abramsky, Mansfield & Barbosa (2011), LIT-277 (NOTE-250); Abramsky, Barbosa, Kishida, Lal & Mansfield (2015), LIT-278 (NOTE-251); Carù (2017), LIT-279 (NOTE-252). The criterion (Prop 4.2 / Prop 16) and the All-vs-Nothing theorem (Thm 21) are proved; the three failures are explicit models, which the readers re-computed exactly over ℤ and ℤ/2. Two steps are the readers’: that the §8 cover and the (2,2,4) model admit no All-vs-Nothing argument over any ring, by Thm 21 read contrapositively. The witness is possibilistic, so it cannot grade anything below strong contextuality. | Active |
| THEORY-527 v5 | If agents are the systems that would adapt their policy were their actions to affect the world differently, then in mechanised causal games meeting Kenton et al.’s five assumptions (one agent per connected component of the decision–utility graph, best response to every mechanism intervention, a fixed tie-breaking order, terminal edges only into decision mechanisms, and mechanism interventions able to set any deterministic function) the game graph, with its decisions, utilities and agents, is recovered exactly from interventions on mechanisms | Kenton, Kumar, Farquhar, Richens, MacDermott & Everitt (2022), LIT-909, read in NOTE-707. The recovery result (Theorem 1) is proved under five assumptions, including the availability of interventions on mechanisms, and was re-derived on promotion (2026-10-20). The definition is a proposal; the verdicts on thermostats and RL are argued from it, and “reliably classifies humans as agents” is asserted. The labels depend on the chosen variables, which the paper states. | Active |
| THEORY-528 | The cases offered for extended cognition are explained at least as well by embedded cognition, on which the organism leans heavily on external props, and memory research finds that external stores lack the interference, generation effect and power-law learning and forgetting of internal memory, so a kind spanning both does no explanatory work and conservatism favours the embedded account | Rupert (2004), LIT-422, read in NOTE-343. The past-endorsement dilemma is strong: without it, directory assistance makes Otto believe every listed number; with it, the organism’s endorsement is the final authority. The memory comparisons are moderate: the internal side is cited research, the external side is thought experiment, and no experiment on an external store is run or cited. The step from “different fine-grained kinds” to “no useful coarse kind” is a challenge plus conservatism. | Proposed |
| THEORY-529 | A state is shown to be a representation by adaptation for transmitting information efficiently, near the optimal trade-off of rate, distortion and coder complexity under a teleofunctionally fixed distortion measure, rather than by correlation or mutual information alone, which nearly any causal link supplies and which cannot increase along a processing chain | Martínez (2025), LIT-149, read in NOTE-165: a position paper with no new theorem or data. Its sharpest point is a standard result: by the data-processing inequality, mutual information about a car/no-car decision can only fall from retina to IT, so a mutual-information criterion would place the decision at the earliest stage; explicitness is better read as ease of decoding. The rest is a proposal supported by selected examples. Complexity has no operational measure, teleofunctions are needed to fix the distortion measure or every system is efficient for some loss, and misrepresentation and engineered systems are not addressed. | Proposed |
| THEORY-530 | The spectrum of a matrix bounds the norm of its rational functions up to a constant only if the matrix is diagonalisable, with the eigenvector condition number as the constant, while the closed numerical range of any Hilbert-space operator does so with a universal constant between 2 and 11.08, exactly 2 for 2×2 matrices | Badea & Beckermann (2013), LIT-011, a handbook survey read in full in NOTE-009. Example 107.2.5: σ(A) is K-spectral iff A is diagonalisable, with K ≤ cond(V). Fact 107.7.2: the closure of W(A) is completely K-spectral for every bounded A with a universal K ∈ [2, 11.08], and 2 suffices for 2×2. The chapter proves almost nothing itself; the numerical range result is cited to Crouzeix (2007). The bound 11.08 was the 2013 state; a later improvement to 1 + √2 is recalled in the reading but not verified. Whether the constant is 2 was open. | Active |
| THEORY-531 v2 | Told in the third person, a transfer of memories and character between two bodies reads as the persons exchanging bodies; told in the first person, no predicted psychological change removes the subject’s reason to fear pain to his own body, and the step that completes the exchange happens only to the other man, so the two tellings support opposite criteria | Williams (1970), LIT-462, read in NOTE-387. The strongest step is shown given its premise: the last step of the series that turns amnesia into a body exchange changes nothing for the subject. The premise, that psychological change cannot remove the reason to fear pain, is argued from cases. Williams claims no criterion of identity, calls his resolution “rather shaky” and “risky”, and does not treat fission. | Proposed |
| THEORY-532 | Systems pushed from equilibrium develop structures that degrade the applied gradient faster, and living systems and maturing ecosystems are such structures, continuous with convection cells and vortices, so the second law is a necessary but not a sufficient condition for life | Schneider & Kay (1994), LIT-533, read in NOTE-415. A “restated second law” (systems moved from equilibrium “utilize all avenues available to counter the applied gradients”) is offered as a corollary of Kestin’s equilibrium stability result and not derived from it. Bénard convection and a draining vortex show organized structures raising dissipation. One stressed marsh, airborne thermal scans and a satellite comparison are read as ecosystems developing to degrade more sunlight; all are correlational and confounded with water. The reading judged the claims too weak to source a THEORY; filed as Proposed. The paper itself says thermodynamics cannot tell the living from the non-living. | Proposed |
| THEORY-533 | When a President can end a funding lapse selectively, paying the parts of government he favours from funds named by no appropriation, a shutdown stops checking him and instead hands him the choice of what to fund; each payment left unchallenged becomes a precedent, and a Speaker who lets it stand gives up his own chamber’s power of the purse | Moynihan (2026), LIT-061, a commentary post read in NOTE-084. The memo of 27 March 2026 directs payment of TSA staff from “funds that have a reasonable and logical nexus to TSA operations”, citing 31 U.S.C. 1301(a) but naming no account; that much is confirmed. That the payment is illegal rests on quoted scholars, with no GAO or court ruling, and the post does not engage the memo’s own appeal to §1301(a). The binary choice it gives the Speaker is the author’s framing. | Proposed |
| THEORY-534 | The optimality of maximum likelihood was never one theorem: each historical proof holds under conditions its author left implicit, and of the classical counterexamples the practically important one is a parameter count growing with the sample, while Hodges-type superefficiency is confined to a set of measure zero | Stigler (2007), LIT-044, read in full in NOTE-074. Fisher’s 1922 proof rests on sufficiency, his 1925 proof on exact normality, and his private 1930 proof on multinomial data and smooth degree-0 estimators. Rigorous treatments (Wald 1943, Cramér 1946) came at the cost of unwieldy conditions. Neyman–Scott, where the MLE of σ² tends to σ²/2, is the failure Stigler weighs as practical; Hodges’s superefficiency is possible only on a Lebesgue-null set (Le Cam 1953). It is a history: the theorem statements are reconstructions, and it says nothing about modern overparameterized models beyond one hedged warning. | Active |
| THEORY-535 | Quantum systems read as bundles of property-instances with no principle of individuality can have their kinds and their number stated in quasi-set theory, so that N indistinguishable particles get a definite quasi-cardinal without labels; the construction covers kinds and counting only, not states, actualization or dynamics | Holik, Jorge, Krause & Lombardi (2021), LIT-107, read in full from the preprint in NOTE-127. The Lombardi–da Costa ontology of properties makes a quantum system a bundle of instances of universal type-properties, with no principle of individuality. Krause’s quasi-set theory Q, reinterpreted over property-instances, represents an atomic bundle as a qset taking one instance from each qset of indiscernibles, guaranteed by Q’s Axiom of Choice, and N particles as a subqset of quasi-cardinal N. The new formal content is about two pages (§6), the printed proofs contain errors, and states, actualization and dynamics are not formalized. The claims about Kochen–Specker and non-separability are recharacterizations by definition, not results. | Proposed |
| THEORY-536 | A group agent’s attitudes are real and non-redundant: each group belief needs members’ role-based acceptance, by assent in the group’s name or by acting on it in an executive role, but that acceptance does not explain or reduce the group belief, because which members’ acceptance counts, and that it plays the role of belief, is fixed only from the group-level view | List & Pettit (2012), LIT-730, their replies to an Episteme symposium on Group Agency, read in NOTE-582. The claim is argued in a few pages against one commentator, Sylvan, whose paper was not read, and it points to the book (LIT-391, unread). The authors grant that non-redundancy is a matter of degree and that the book takes the existence of group agents “mostly … for granted”. A position on explanation, not a proof, and not a claim that groups have experiences. | Proposed |
| THEORY-537 | Warrant for a type-level causal claim in biomedical and social science comes from eliminating the relevant alternative accounts of its support, not from the kind of study that produced the data, so a randomised trial earns its standing only by eliminating many alternatives at once | Reiss (2015), LIT-118, read in NOTE-197 from the 2015 Durham working paper; the refereed version was not read. A conceptual proposal with one historical illustration, the 1950s smoking and lung cancer controversy, which the author says is not a test. What counts as relevant, and when to stop probing, is handed to context, and the four grades of warrant are admitted to be arbitrary. | Proposed |
| THEORY-538 | A system believes and desires when its behaviour is reliably and voluminously predictable by treating it as a rational agent with the beliefs and desires it ought to have, and the success of that strategy is an objective fact though adopting it is free; the more richly a system is connected to its world, the fewer interpretations fit, so thermostat and person differ in degree | Dennett, “True Believers”, LIT-398, read in NOTE-353 in the revised text of 1987/1997. The criterion is substrate-neutral and silent on experience. Its adverbs are not quantified, the lectern is excluded only by gain over a baseline the essay leaves informal, and the Martian argument is an intuition pump that assumes the intentional patterns are not captured physically. “Most beliefs are true” rests on a way of counting beliefs Dennett doubts exists. Proposed, and a rival of both Block’s psychologism and Searle’s causal-powers account. | Proposed |
| THEORY-539 | Moral judgment draws on several innately prepared intuitive foundations, at least Care, Fairness, Loyalty, Authority and Sanctity, each a response to a different adaptive challenge, and Sanctity descends from pathogen avoidance rather than from cooperation | Graham, Haidt et al. (2013), LIT-499, read in NOTE-396; its first statement, Haidt & Joseph (2004), LIT-502 (NOTE-400); and the MFQ-2, Atari et al. (2023), LIT-500 (NOTE-398). Pluralism has moderate support. The particular list does not: its evidence table gives Sanctity no primate or infant evidence and Authority no infant evidence, the foundations were matched to existing evolutionary models rather than derived, and the disgust findings behind Sanctity were later disputed. | Proposed |
| THEORY-540 | For moral purposes the body is bounded below by depth: objects whose real definitions are too microphysically committal are not body parts though they are parts in the ordinary sense, and bodily rights and interests concern only events that change the body’s high-level properties, so a brain-computer interface user’s implemented software can be a body part while the third-party server running it is not | Register (2025), LIT-138, read in full in NOTE-151. An argument from cases. It assumes that BCIs can be body parts and that no part of a person may be owned by another, and uses depth to reconcile the user’s unqualified bodily ownership with the operator’s property in the server. The two moral principles are its operative premises, and it says they do not depend on the real-definition ontology, which only explains them. The threshold for “high-level” is context-sensitive and unfixed, and the step that software and server are distinct coinciding objects is hedged. The conflict over servers is narrowed, not dissolved. | Proposed |
| THEORY-541 | A model of discovery or analogy that is given representations built with the answer in view has been given most of the answer, as BACON was with Kepler’s data and SME with its solar system and atom, and representation-building cannot be postponed to a separate module, because which representation is right depends on the task and on the analogy being made | Chalmers, French & Hofstadter (1992), LIT-414, read in NOTE-359 from the preprint, with Burns’s review of Fluid Concepts (1995), LIT-457, read in NOTE-375. The BACON critique is strong; the SME critique moderate, with no alternative encoding run; the two arguments against a representation module informal. Burns turns the charges on Copycat: its Slipnet holds the domain’s relevant relations, and the symbol-grounding objection to SME applies to it equally. Nothing is measured in either text. | Proposed |
| THEORY-542 | A word learner that infers speakers’ referential intentions jointly with the lexicon, and lets words be uttered non-referentially, learns object names from child-directed video more precisely than co-occurrence and translation models, and mutual exclusivity, word-guided object individuation and intention-guided mapping follow from it without principles built in for them | Frank, Goodman & Tenenbaum (2009), LIT-815, read in NOTE-611. On about twenty minutes of video from two dyads, annotated by the authors, the intentional model’s lexicon scores precision .67 and F .55 against .06–.15 and .10–.22 for five baselines. The behavioural fits are qualitative, the baselines also produce mutual exclusivity, and the Baldwin case supplies the intention rather than inferring it. The reading said no THEORY, because the findings are specific to a small corpus and the record held nothing they correct; this account is filed Proposed for that reason. | Proposed |
| THEORY-543 | Diffusion can destabilise a homogeneous steady state of reacting chemicals that is stable without it: a disturbance of one finite wave-length grows while uniform and very short ones decay, so a stationary pattern appears whose spacing is set by the reaction and diffusion constants and only its phase by the disturbance; with two substances this needs them to diffuse at different rates, and the pattern lasts only while free energy is supplied | Turing (1952), LIT-535, read in full in NOTE-427, with Cross & Hohenberg (1993), LIT-527, skimmed in NOTE-418. The linear analysis on a ring gives exact conditions (9.4a, b) for stationary waves of finite wave-length; that equal diffusibilities cannot satisfy them is NOTE-427’s substitution, not stated in the paper. Turing calls the linearity assumption “a serious one” and the biological examples “very limited”. Stationary chemical Turing patterns were first made in 1989–1991, and real morphogens implementing the mechanism had not been identified by 1993. | Active |
| THEORY-544 | In homotopy type theory extended with a strict directed interval and a layer of shapes, one contractibility condition, the Segal condition, gives a type identities, associativity and three-dimensional coherence, makes every function between Segal types a functor, and yields a dependent Yoneda lemma for covariant families; that such types are (∞,1)-categories rests on a semantics only sketched | Riehl & Shulman (2017), LIT-032, read in full in NOTE-069. The internal results of §§5–11 are proved: associativity from the Segal condition applied to A^2 (Prop. 5.9), inner 3-horns (Prop. 5.21), functoriality of every function (Prop. 6.1), the dependent Yoneda lemma (Thm 9.5), and uniqueness of left adjoints into a Segal type from a Rezk type (Thm 11.23). Segal and Rezk types match Segal and complete Segal spaces (Props A.21, A.25), but soundness of the type theory in bisimplicial sets is sketched and depends on an unproved initiality theorem. Coherence in all dimensions is conjectured, not proved. | Active |
| THEORY-545 | Aerts and Gabora’s founding quantum model of concepts is a classical probability model written in a Hilbert space: every context it uses is a projector diagonal in one basis, so the contexts commute and generate a Boolean algebra, its entangled ‘pet fish’ state gives the same statistics as a classically correlated mixture for every context in the model, and its guppy weights are copied from single-concept ratings rather than predicted for the conjunction | Aerts & Gabora (2005), Parts II and I, LIT-312 and LIT-340, read in NOTE-299 and NOTE-294. The structural facts are checks of the published model, not of the authors’ prose: contexts are sums of basis projectors, counts are chosen to match rounded frequencies, and the authors call the result a “quantization” of a set-theoretical model. Part I’s mark of non-classicality (eq. 19) is met by Boolean projection lattices too, and its lattice structure is supposed, not derived. The model as printed is also infeasible in two cells. It does not say that no quantum model of concepts does better. | Active |
| THEORY-546 v2 | A person persists by psychological continuity, not by sameness of substance or of the human animal; Locke’s sameness of consciousness, which he leaves undefined, meets the charges of circularity, intransitivity and gaps when recast as overlapping chains of causally dependent psychological states with quasi-memory, and fission then needs either a clause against branching or multiple occupancy | Locke (1694), LIT-464, read in NOTE-385, with the repairs as Olson’s survey (LIT-454, NOTE-374) and Parfit (LIT-447, NOTE-378) give them. Locke shows that same man, same substance and same person can be given different conditions; that the person’s are those of consciousness he asserts and illustrates. The repaired criterion is the majority view in the survey, and its author, an animalist, argues it implies two thinkers in every chair. It is a criterion of persistence, not an account of what matters or of what we are made of. | Proposed |
| THEORY-547 v2 | A language model idealized as continuing any text with a plausible next word from the collection of all plausible texts follows narrative coherence and not truth, so its false statements are confabulations within the story the context sets up; whether trained and aligned chat models keep that nature is an open empirical question the idealization does not settle | Bottou & Schölkopf (2023), LIT-178, read in NOTE-102: an essay offering imagery, with no evidence beyond one Vicuna-13b transcript pair. For the “perfect language model” it defines, insensitivity to truth follows from the definition. That deployed chat models share it is assumed, and the essay’s own §2 leaves open whether alignment can turn a fiction machine into a verification machine. It credits the machine with knowledge of what makes sense in the story, denies it truth-directedness and intention, and never uses the word “sycophancy”. | Active |
| THEORY-548 v2 | In generalised Lotka–Volterra dynamics with every interaction delayed by τ, a feasible equilibrium that is stable without delay loses stability at τ_c = min over the community eigenvalues j of arctan(|Re j|/|Im j|)/|j|, where a pair of roots crosses the imaginary axis transversally (a Hopf point), so the critical delay is set by the community spectrum; in Saeedian et al.’s strongly self-regulated setting the oscillating regime’s community-level variability falls with diversity (S = 10–70) while species-level variability rises, and the fall matches what summing independently oscillating species gives | Saeedian et al. (2021), LIT-057, a preprint, read in NOTE-061. The critical delay is the linear delay result on the community matrix, re-derived on promotion (2026-10-20), and matched simulation at one strongly self-regulated setting. The variability result was re-run on promotion against an averaging null and matches it: the fall of community-level variability with diversity is what summing independent oscillators gives, not an ecological stabilisation. | Active |
| THEORY-549 | A structured group is not identical to its members: two groups of one kind can have the same members at every time and still be two, which theories that identify a group with a plurality, fusion, aggregate or set of its members cannot allow, and a view of groups as realizations of structures with functionally defined nodes can | Ritchie (2013, online 2012), LIT-479, read in NOTE-390, with its 2018 sequel LIT-486 (NOTE-389). Six criteria for a theory of groups, each defended by one example, rule out non-singular pluralities, Sider’s fusions, Burge’s aggregates and Effingham’s sets; the decisive one is Coincidence. Groups as realized structures meet all six. The refutations are strong given the criteria; the criteria rest on single cases, and the positive view is a four-page sketch with no persistence conditions. It says nothing about agency or minds. | Proposed |
| THEORY-550 | Unsupervised clustering is not made epistemically superior to supervised classification by the absence of labels: it is sensitive to sample bias, highly sensitive to how inputs are represented, and overfits, with the number of clusters acting as a capacity control just as parametric complexity does in supervised learning | Søgaard (2024), LIT-162, read in NOTE-108. A rebuttal of two arguments for clustering’s superiority, the No-Bias Argument and the Simplicity-Truth Argument, by toy counterexample and by the technical literature on overfitting in unsupervised learning (Hansen & Larsen 1996). The negative claims are firm. The paper’s positive step, that supervised classification is “at least as” justified, is under-argued and is not part of this account. | Active |
| THEORY-551 | The Russian narrative of a Western information war waged against Russia since the Cold War was politicised by academics, politicians and the public each for their own reasons, scholars promoting their ideas, politicians consolidating power and a public wanting its lost national pride explained, and not directed from the Kremlin; once adopted into rhetoric, doctrine and law, it drives behaviour whatever its origin | Fridman (2017), LIT-088, read in NOTE-070, traces the narrative to Messner, Dugin and Panarin and follows it into Putin’s and Lavrov’s rhetoric, the 2015 National Security Strategy, five laws and Levada polling. That it is present in official discourse is strongly supported; that its politicisation was not Kremlin-led rests on chronology that fails for Dugin, and the doctrine-to-law order is reversed for four of five laws. Clark (2020), LIT-023, read in NOTE-012, finds the same belief in military writing and also rejects the merely-cynical reading. The two share no evidence. | Proposed |
| THEORY-552 | Indeed’s US software-development job-postings index rose to 233.8 in February 2022 and fell to 65.2 by mid-February 2025, measured against 1 February 2020 = 100, while all postings stood near 110; it was the deepest fall of any Indeed sector, though not the only one to have more than doubled, and the postings data cannot apportion the fall among interest rates, over-hiring and AI | Orosz (2025), LIT-089, read in full in NOTE-039, which checked the figures against Indeed Hiring Lab’s own published series (current vintage). The headline numbers reproduce: 65.2 on 2025-02-13, a 3.59× fall from the peak, −8.3% year on year, all postings 109.5. Several side claims do not: the baseline is 1 February 2020, not January; the peak was February 2022, not mid-2022; six sectors peaked above 200. The index counts active postings, not vacancies or hires, and the post’s ranking of causes is informal. | Active |
| THEORY-553 | In the Döring–Isham topos representation of quantum theory a bounded physical quantity cannot take values in the topos’s real-number object; it is represented faithfully by an arrow from the spectral presheaf to a presheaf of monotone real functions over subcontexts, so its value at a context is a spread that widens as the context shrinks, and these values form only a commutative monoid, under which sums of daseinised quantities are not daseinisations of sums | Döring & Isham, paper III (2007/8), LIT-299 (NOTE-290), restated with additions in LIT-378 (NOTE-326). The Gel’fand transforms of daseinised operators grow as contexts shrink, so arrows into the constant presheaf ℝ are impossible (3.3–3.4). Each  gives a natural transformation δ̆^o(A) : Σ → ℝ^⪰ (Thm 3.1), and  ↦ δ̆^o(A) is injective, by de Groote’s results. ℝ^⪰ is a monoid, not a group; differences need a group completion, whose global elements are the functions of bounded variation on the context poset. No choice among the candidate value objects is made, and the state-dependent reading of the spread is cited, not proved. | Active |
| THEORY-554 | On the grounds of moral standing now commonly accepted, together with scientific premises that are not unreasonable, the aggregate interests of insects or the interests of near-future AI could outweigh humanity’s; no capacity yet proposed secures human priority, and the books that state those grounds retreat to moderate advice without a principle that supplies the stopping point | Schwitzgebel & Sinnott-Armstrong (2026), LIT-166 (NOTE-116), with the SEP survey of animal moral status (LIT-146, NOTE-181) for the failure of capacity-based human exceptionalism. A conditional, defended as one: the reviewers “take no stand on ponens vs. tollens” (p. 6) and do “not endorse” the radical conclusion (p. 38). The scientific premises are called “not unreasonable” and not argued, so the account is only as strong as they are. | Proposed |
| THEORY-555 | In London in 2018, Airbnb listings that were possibly breaking the 90-night short-let cap, defined as entire homes offered for more than 180 days a year by hosts with two or more listings, were about 0.16% of the housing stock (about 5,300 homes) but 3.5–7% in a few central small areas, and across small areas they correlate weakly with flats, private renting and low dwelling-type diversity | Shabrina, Arcaute & Batty (2021), LIT-094, read in full in NOTE-071. A descriptive estimate from Inside Airbnb and VOA counts under a proxy that rests on availability, not bookings, and on an untested 50% occupancy. The abstract’s “more than 2% … misused” is the share listed at all, not the share possibly misused. The paper’s borough rent result (n = 33, cross-sectional) and its “8% per doubling” translation do not belong to this account and should not be cited as an effect size. | Active |
| THEORY-556 | Clustering, abstraction and generative modelling can be how we come to identify natural kinds, essential properties and unrealized possibilities, but kinds, essences and possibilities are not by definition what such algorithms would find under ideal conditions, because nothing guarantees they are effectively computable; so an algorithm’s output is evidence about a kind, neither objective nor vacuous, and not what makes it one | Watson (2023), LIT-187, read in full in NOTE-172. Three pairs of theses, one per task: the epistemic one (EC, EA, EG) accepted, the ontological one (OC, OA, OG) rejected, each on the same computability ground. The rejection is a bare possibility argument with no example of an uncomputable kind, and the acceptance is hedged (“or something very much like them”) so far that it is hard to falsify. The pragmatic, context-relative view of kinds is asserted, not defended. Self-supervised learning and foundation models are outside its scope. | Proposed |
| THEORY-557 | Low-loss paths between independently trained solutions are found outside supervised image classifiers: graph neural networks trained from different seeds on one graph are joined by quadratic Bezier curves where the straight line has a barrier, and one pair each of diffusion and contrastive models by chains of low-loss checkpoints | Li et al. (2025), LIT-676, read in NOTE-529: GCN node classifiers from different seeds, on 12 real graphs and synthetic CSBM graphs, show linear barriers that a fitted quadratic Bezier curve removes. Yao, Zhang & Tian (2026), LIT-660, read in NOTE-534: one pair of DDPMs and one pair of small CLIP models joined by chains of checkpoints whose training loss stays under a threshold, where AutoNEB’s paths rise steeply on CLIP. The evidence is plots without barrier numbers in the first, one pair per model and retrained anchors in the second. Zhang & Blei’s claim of flat paths between LDA’s ELBO maxima (LIT-677) reports no results. | Proposed |
| THEORY-558 | Moral judgment is usually caused by quick affective intuitions, and moral reasoning is usually a post-hoc search for supporting reasons that changes judgments mainly by triggering intuitions in other people | Haidt (2001), LIT-511, read in NOTE-403: the social intuitionist model. Its case rests mostly on non-moral evidence about automaticity, motivated reasoning and confabulation, carried over by argument. Its direct moral evidence is that harmless taboo violations are condemned and that affect predicts the condemnation better than perceived harm. The author calls it “a plausible alternative”, not “an established fact”. The disgust manipulations that were its direct causal evidence were later disputed. | Proposed |
| THEORY-559 | In Kolmogorovian probability, joint distributedness is transitive, so representing a measurement by one random variable in every context it occurs in already puts all measurements of a connected system on one probability space; within that representation a Kochen–Specker or Bell contradiction refutes the context-independent identification of measurements, not the existence of a joint distribution | Dzhafarov & Kujala (2017), LIT-836, read in full in NOTE-623. The transitivity step is an elementary proof; the reading of the reductio is an argument that rests on it. It binds the random-variable representation only: the sheaf account keeps one variable per measurement and asks whether marginals glue, and a reader who holds that view is not bound by it. The paper also proves that a coupling of a binary connection is multimaximal iff adjacent pairs, ordered by their means, are maximally coupled (Theorem II.3). | Active |
| THEORY-560 | In rodents, gut microbes can drive stress and affect-related behaviour through vagal, immune, endocrine and metabolite routes, and faecal transplant from depressed people partly transfers the phenotype; in people, probiotics have so far shown at most small reductions in subjective stress in healthy volunteers, and strains with strong preclinical records have failed in controlled trials | Forssten et al. (2022), LIT-915, read in NOTE-703. A narrative review with no search method, by employees of a probiotics manufacturer, which documents its own translational failures: L. rhamnosus JB-1 had no effect on any outcome against placebo after “comprehensive preclinical evidence”. The rodent half is well documented; the human half rests on one meta-analysis of healthy volunteers and trials with nulls. Proposed because the source is a narrative industry review; the gap it describes runs against its authors’ interest. | Proposed |
| THEORY-561 | If moral evaluation has thresholds below which effects are negligible, a system of agents can do good or evil that none of its members’ interactions does, and the same thresholds make an environment tolerant of small evils and inert to small goods; on the examples offered the non-additivity lies in the evaluation, as a step function of summed impact, not in the actions | Floridi (2013), LIT-901, read in NOTE-698. A model with two moral thresholds and four positive examples; it proves nothing and reports no data. That morally loaded wholes can arise from negligible parts follows once thresholds are granted, and the reading rates it moderate. The analogy with distributed knowledge is inexact: every example sums like contributions, the threshold’s value is left open, and so the line between distributed morality and a sum of loaded acts is a free parameter. Responsibility for such outcomes is not given here. | Proposed |
| THEORY-562 | In REST2 replica-exchange simulations of intrinsically disordered proteins, high swap acceptance and short round trips show that replicas mix along the temperature ladder, not that conformations are sampled, because the upper rungs collapse the chain; sampling shows only when independent demultiplexed replicas agree in their structural distributions | Koneru, Reid & Robustelli (2025), LIT-076, read in full in NOTE-076. A how-to chapter whose one load-bearing methodological point is that high swap acceptance “is not, in isolation, sufficient evidence of robust conformational sampling or convergence” (p. 18). The reason the reading draws out is that REST2’s upper rungs are unphysical Hamiltonians on which disordered chains over-collapse, so replicas can swap freely without the chain rearranging. The chapter argues this and shows a passing example; it shows no failed run, and its convergence criteria have no quantitative threshold. | Proposed |
| THEORY-563 v2 | Consciousness is a real pattern in the brain’s content-bearing states, a description that trades predictive accuracy for compression, and so coarse that describing the brain through it is metaphor; on that reading there is no Cartesian theatre, whether a given content was conscious can lack an answer when two descriptions compress and predict equally, and first-person reports are fallible as literal descriptions of the brain but authoritative as an author’s | Taylor (2024), LIT-461, read in full in NOTE-379. An interpretation of Dennett offered as consistent, explicitly not as correct or as what Dennett meant. Its argument for indeterminacy in masking rests on Dennett’s idealised description of the cases, which Taylor calls “somewhat simplistic”. It does not say which real pattern consciousness is, or what makes a real pattern a conscious one rather than a belief pattern. Filed as the account the reading states, at the strength the reading gives it. | Proposed |
| THEORY-564 v2 | A bounded generative model can learn its own structure with no machinery beyond inference and learning: spare hidden-state slots with flat likelihoods get filled when an observation fits none of the learned causes, and Bayesian model reduction on the learned prior over states can return unneeded slots, though in a toy concept-learning task it recovers the true number of causes in only 45–80% of runs with four to seven causes, and never with two or three, unless the likelihood is given | Smith, Schwartenbeck, Parr and Friston (2020), LIT-615, read in NOTE-485. Expansion works in the toy domain over eight runs per condition, and only for novel stimuli. Reduction is the weak half: over 100 runs, the true number of concepts won in 45–80% of runs for four to seven, never for two or three, and in every run when the likelihood was given. Table 1 is the record’s only measurement of how often reduction picks the generating structure when the parent model was itself learned. One initialisation; eight concepts, six binary features. | Proposed |
| THEORY-565 v3 | From a symmetric, positivity-preserving, positive semi-definite affinity, the normalized Markov operator is conjugate to a symmetric one, so its leading eigenfunctions scaled by powers of their eigenvalues embed the data with Euclidean distance equal to diffusion distance, and a density-corrected normalization recovers the Laplace–Beltrami operator independently of how the data were sampled | Coifman et al. (2005), LIT-981, read in full in NOTE-1441. The finite construction and its isometry are THEORY-728; the paper’s own diffusion distance is the one ã^(m) induces, not the inverse-stationary-weighted one. Theorem 2.1 and the α-family are stated without proof; the companion (LIT-1246, NOTE-985) proves the α-family’s limit, Active without boundary as THEORY-744, and its heat-kernel step is QUESTION-231. Self-adjointness comes from the kernel’s symmetry, and “directed diffusion” is anisotropic, not a non-reversible chain. | Proposed |
| THEORY-566 v2 | In Ganea et al.’s hyperbolic neural networks, linear maps and nonlinearities are Euclidean ones read through the chart at the origin, so a stack of them without biases is a Euclidean network conjugated by that chart, and the curvature acts only through the bias translations and the distance-based output layer | Ganea, Bécigneul & Hofmann (2018), LIT-879, read in NOTE-686, which checked the closed forms numerically. Möbius layers are defined as exp₀ ∘ f ∘ log₀, so any composition of them is exp₀ ∘ (the Euclidean composition) ∘ log₀, as the paper notes; only the Möbius bias, which is parallel transport from the origin followed by the exponential map, and the hyperbolic logistic regression’s distances to geodesic hyperplanes are not absorbed by the chart. The structural fact is proved; that the networks’ gains, confined to a synthetic task and to separating WordNet subtrees in low-dimensional Poincaré embeddings, come from those two operations is this record’s inference. NOTE-686 filed no THEORY. | Active |
| THEORY-567 | In the donation game, where a cooperator pays c for another to get b, defectors win in a well-mixed population, and each of five mechanisms makes cooperators evolutionarily stable above a benefit-to-cost threshold: kin selection r > c/b, direct reciprocity w > c/b, indirect reciprocity q > c/b, network reciprocity b/c > k and group selection b/c > 1 + n/m; the rules cover altruism only, not mutualism, coordination or conflict | Nowak (2006), LIT-501, read in NOTE-409, main text only. A four-page review that casts each known mechanism as a 2×2 game so that one set of criteria applies to all. The five ESS conditions are confirmed by the main text; the derivations are in the supporting material, which was not read, and in cited papers. Several rules hold only under weak selection, regular graphs or rare group splitting. Every mechanism is modelled with the donation game, so mutualism, coordination and conflict are outside it. | Active |
| THEORY-568 | Whatever redundancy measure a partial information decomposition uses, provided its atoms satisfy the consistency equation, the average number of single sources an atom can be read from is Σᵢ I(Xᵢ;Y)/I(X;Y) and the average number of sources it cannot do without is Σⱼ I(Xⱼ;Y|X₋ⱼ)/I(X;Y); so the redundancy–synergy index equals (r̄ − 1)·I(X;Y), and for three or more sources it counts a k-way redundancy k − 1 times but synergy once | Gutknecht et al. (2025), LIT-042, read in full in NOTE-045, with the combinatorial proofs of Props. 1–4 and 6 checked by hand. The averages need only the consistency equation and I(X;Y) > 0; reading them as average degrees, and the bounds of Appendix B, need non-negative atoms. Corollary 5 overstates Prop. 6 (⇔ for ⇐). The network results are on tiny quantised models evaluated on their own training sets, and are not part of this account. | Active |
| THEORY-569 | Measured as the contrast between a set of explanantia’s CohOG+ coherence with the explanandum and with its negation, explanatory power satisfies Roche and Sober’s Two Likelihood Inequalities for single hypotheses and fails the One, and in one causal chain and one collider it ranks the richer set above the sparser over a range of priors, where no two-place TLI measure can rank a conjunction so | Hartmann & Trpin (2026), LIT-165, read in NOTE-168, which recomputed all three numerical claims. One theorem (TLI for singleton explanans sets), one counterexample (OLI fails) and two parameterised existence examples (a distal cause for P(H1) < .7; a negatively interacting cause for P(H1) = P(H2) < .75). The escape from Roche & Sober is representational: a set is scored differently from the conjunction, and the two-place theorems still hold for conjunctions. No characterisation says when the richer set wins, and the paper’s claim that the measure “accommodates key scientific judgments” is more than the body shows. | Active |
| THEORY-570 | An emotional state is a large-scale selection of mental resources, switched on and off by Selectors that Critics trigger on recognising a type of problem, and so of the same kind as an intellectual way to think; feelings are the mind’s descriptions of these cascades, and the body is one more resource the brain uses, not the substance of emotion | Minsky (2006), The Emotion Machine, LIT-432, read in NOTE-348 from the author’s 2005 draft. A design argued from examples, thought experiments and the author’s own AI programs, with no experiment; Minsky marks several parts as his untested conjecture. It disagrees directly with the body-state views of emotion and of feeling. On Elliot it proposes the reverse causal order to Damasio’s, with no evidence offered. | Proposed |
| THEORY-571 | A brain state is better characterised by how its activity moves among a repertoire of weakly coupled metastable substates on a landscape constrained by the structural connectome, their occupancy, dwell times and transitions, than by static connectivity; health is a metastable balance, depression a landscape of over-deep attractors and psychedelic states a flattened one, at opposite ends of one spectrum | Vohryzek, Cabral, Vuust, Deco & Kringelbach (2022), LIT-080, read in full in NOTE-054. A perspective that reports no data: the landscape (Fig. 6) is illustrative, adapted from earlier work, and no study measures depressed and psychedelic states on a common scale. The psychedelic evidence is small cited studies of broader substate repertoires and higher signal diversity; the depression evidence is three studies, one in remitted patients, though the abstract calls depression “excessively rigid”. The modelling section is heavily self-citing. Proposed: a framing, with the record’s rival description of the same dynamics as continuous in THEORY-088. | Proposed |
| THEORY-572 | Where an effect is not yet well conceptualised, replication cannot say which effect exists: direct replication bears on random error, conceptual replication presupposes that two operationalisations pick out the same effect, and an effect is delineated instead by probing for systematic error | Feest (2019), LIT-161, read in NOTE-196 from the PSA 2018 manuscript; the version of record was not read. An informal argument with one historical case, the Mozart effect, declared “typical” without further evidence. The claim that direct replication says “nothing” about systematic error is overstated: multi-lab replications vary some tacit lab-level factors. The conclusion is scoped by the author to effects not yet well conceptualised, and to internal validity; the title and abstract drop that hedge. | Proposed |
| THEORY-573 | Signals of processing quality from different senses, such as fluency, familiarity and coherence, pool into one content-nonspecific feeling, and that pooled feeling contributes to the unity of conscious experience across modalities, alongside the integration of specific features; in support, coherence in one modality shifts judgments of regularity, familiarity and possibility about unrelated targets in another | Winkielman, Ziembowicz & Nowak (2015), LIT-190, read in full in NOTE-146. An opinion piece whose main evidence is the authors’ own three experiments (Ziembowicz et al. 2013), summarised without statistics and not read by the record. The authors state that direct evidence is still needed that the effects run through changed experience and that its integration is causal. No study cited measures unity of experience. The LIT is itself Proposed; this account carries its promotion condition. | Proposed |
| THEORY-574 | The structural width of Xin Li’s learning programme is a covering number of the margin-safe region by local pieces: its lower bounds come from metric confinement through a wedge point, not from topology, labels enter only through the margin, and the error floor below width binds only learners assembled from local experts, so it does not entail routing, nor training routing apart from the task loss | Li (2026), LIT-376 (Local Urysohn Width, v1), LIT-375 (Structural Learning Theory) and LIT-374 (Structural Decoupling), read jointly in NOTE-323, NOTE-324 and NOTE-322. In repaired form the formal core holds: width is incomparable with the per-cell VC dimension, fewer cells than width give an error floor (under an assumption that states it), and discovering all basins costs Ω(w log w) samples. But local correctness is automatic on any connected patch, the bouquet lower bound is metric (the paper’s Remark 8.11 concedes it), a global classifier has width 1 (Remark 3.4), and the additive Rademacher bound said to call for decoupled training holds for joint training too. | Active |
| THEORY-575 | ’Social group’ names two kinds of thing: organized social groups, such as teams, courts and families, are structured wholes whose people occupy the nodes of an internal social structure, while feature social groups, such as women, racial groups and classes, are social kinds, nodes in external social structures, and are not concrete wholes | Ritchie (2020, online 2018), LIT-486, read in NOTE-389, building on her 2013 view (LIT-479). A social structure is one constitutively, not merely causally, dependent on social factors. Organized groups realize internal structures; feature groups are positions in external ones, which can be intersectional. A framework offered to “motivate”, in the author’s word: accounts of gender are shown to fit it, not argued for against rivals, and the work of excluding arbitrary collections is done by a restriction the framework imports. Silent on agency; the record uses it to say which groups the agency questions are about. | Proposed |
| THEORY-576 | In a bundled network, one fiber graph attached at a single node to every node of a base graph, the low Laplacian spectrum is the base spectrum divided by the fiber size to first order, so the gap exponent (Fiedler dimension) is set by the base while the density-of-states exponent (spectral dimension) is the fiber’s; the two come apart generically and coincide only in special cases, and relaxation then decays with the spectral dimension at intermediate times but equilibrates on a time set by the Fiedler dimension | Grimaldi, Villegas, Vezzani, Burioni, Cassi & Gabrielli (2025; PRE Letter 2026), LIT-028, read in full with its SM in NOTE-005, which re-derived the key steps and checked them numerically on the comb. λ_{n1} = ℓ^b_{n1}/N_f gives d_g = 2(d_f,f + d_f,b)/(d_f,f + 2d_f,b/d_g,b) in the base-controlled regime; d_s = d_s,f is earlier work by the same group. The comb has d_s = 1 and d_g = 4/3. Proved for one graph class only; the paper’s composite finite-size scaling prefactors (SM Eqs. 25, 29) are wrong, and its “generic property of composite architectures” outruns the proof. | Active |
| THEORY-577 | Our judgments that consciousness poses a hard problem are behaviour, so explaining them is an easy problem that can be solved without mentioning consciousness; and a theory that names a mechanism as the basis of consciousness owes an account of how that mechanism produces those judgments, which IIT and biological theories struggle to give, since a functional duplicate with zero integrated information, or in silicon, would make the same reports | Chalmers (2018), LIT-425, read in full in NOTE-354. The meta-problem follows from the physical explicability of behaviour; the challenge is a constraint argued from it, “not a knockdown argument”. It assumes that a zero-Φ simulation has the same intuitions on a functional reading, which an IIT theorist can deny. The paper’s own favoured solution, opaque introspective models attributing primitive relations of acquaintance, is “closer to a fleshed-out explanandum” than an explanation, and the data the programme needs mostly do not exist. | Proposed |
| THEORY-578 | Between two trained networks that compute nearly the same function, a chain of models minimising the summed Jensen–Shannon divergence between neighbours, a discretised Fisher–Rao geodesic found without labels, can be a low-loss path where the straight line in weights has a barrier | Tan, Long, Zhao & Laine (2023), LIT-662, read in NOTE-521. Two ResNet-20s at 4× width with LayerNorm, CIFAR-10, permuted by Git Re-Basin’s weight matching: the straight line between them still has a large loss barrier, and a chain of 25 models optimised from it to minimise Σ JSD between neighbours on unlabelled training images keeps train and test loss low. One pair, one figure, no numbers in the text. The hypothesis that every geodesic between SGD solutions is mode-connecting is stated, not tested, and a chain whose neighbours agree in output may be low-loss almost by construction. | Proposed |
| THEORY-579 v2 | If belief is individuated by functional role, an external store that is constantly consulted, directly available and automatically endorsed can carry a standing belief, so the material vehicles of some mental states extend beyond the skin; the step from coupling to parthood rests on that premise and a parity principle the authors state rather than argue | Clark & Chalmers (1998), LIT-097, read in NOTE-180, with Clark’s reply to the critics (2005), LIT-403, read in NOTE-363. Otto’s notebook plays for him the role Inga’s memory plays for her, so on role-functionalism it carries his standing belief, and Twin Otto, a duplicate from the skin in, believes otherwise. The constitutive step is carried by role-functionalism, the parity sentence and explanatory simplicity, none of them defended; the four coupling features mark a clear case and are explicitly not necessary and sufficient. Proposed: the step from causal coupling to parthood is the open point. The thesis is about vehicles of standing beliefs, not about consciousness. | Proposed |
| THEORY-580 v2 | On any cover of a space of input histories, the empirical models compatible with a causal structure are exactly the points of a polytope cut from a product of simplices by linear causality equations, so how much of a model a causal structure can explain is a linear program; causal separability is relative to an assumed ambient structure, and the causally separable fraction is never less than the separable local fraction | Gogioso and Pinzani (2023), LIT-788, skimmed in NOTE-624, with the proofs of the causaltope theorems (2.18, 2.19, 2.25) and of the lower bound (2.29) read and checked on promotion (2026-10-20), against the definitions they take from The Topology of Causality. The proofs are short because the work is in the definitions; the one step left implicit closes. The quantum switches witness indefinite order only relative to an ambient space with known no-signalling constraints, not absolutely. | Active |
| THEORY-581 v2 | Two exactly consistent descriptions of one system, at different scales and with equal past–future mutual information, can differ in how that information divides between redundancy and synergy; in small generated Boolean networks under the Williams–Beer redundancy measure the coarser scale was more synergy-biased in every random stochastic system, by at most about 0.07, and the direction mostly reversed for redundancy-biased deterministic ones | Varley & Hoel (2022), LIT-027, read in NOTE-020. Expanding a 3-node macroscale TPM into 4- and 5-node equivalence-class microscales holds mutual information fixed with zero inconsistency, so any change in the PID’s synergy bias B_syn is a change of type, not of amount. In 200 |Gaussian| TPMs the macroscale gained B_syn by about 0.005–0.07; in 185 near-deterministic ones most with macro B_syn < 0.5 lost it. One redundancy function, no robustness check, tiny constructed systems. The “unifying theory” of the title is a framing: the EI section re-describes a known decomposition and adds no result. | Active |
| THEORY-582 | Causal coupling between a process and something outside it does not by itself make that thing part of the process, so an argument from coupling to extended cognition needs a further premise saying what makes a process cognitive | Adams & Aizawa (2001), LIT-438, read in NOTE-368, and their reply to Clark (2010, read from a draft), LIT-455, read in NOTE-380. A thermostat’s bimetallic strip, the kidney’s filtration and a nerve at a neuromuscular junction are each coupled to more than themselves, and their processes do not extend. The 2010 text names the inference the “coupling-constitution fallacy”. The point is that coupling does not entail parthood. It is not shown that coupling never accompanies parthood, nor that the extended-mind authors relied on coupling alone. | Active |
| THEORY-583 | An agent is the set of parts that pursue a goal together, bounded by the farthest events it can sense and try to regulate; cells joined by bioelectric coupling share measurements and so form larger agents with larger goals without ceasing to be agents, so a living system is many nested agents, not one, and cancer is the larger agent shrinking back to the cell | Levin (2019), LIT-439, a hypothesis-and-theory essay read in full in NOTE-341. A definition of the Self as a goal-pursuing collective, tied to a mechanism, gap-junctional coupling, from cited experiments on patterning and cancer. It has no model, no measurement of the light cone and no new data. Its goals are cybernetic set points, so any homeostat is a Self. Its Self is an agent and an individual, not a subject. The sentence against IIT’s single Self is a bracket, and the closing remarks on experience are labelled speculation. | Proposed |
| THEORY-584 | The quantum fidelity tr√(ρ1^{1/2}ρ0ρ1^{1/2}) is exactly the classical Bhattacharyya overlap of the two states’ outcome distributions minimized over all measurements, and the minimum is attained by a projective measurement whose eigenvalues are square roots of likelihood ratios | Fuchs (1995), LIT-018, read in full in NOTE-021. min over POVMs of Σ_b √(tr ρ0E_b)√(tr ρ1E_b) equals tr√(ρ1^{1/2}ρ0ρ1^{1/2}) (Eq. 3.28), attained in the eigenbasis of M = ρ1^{-1/2}√(ρ1^{1/2}ρ0ρ1^{1/2})ρ1^{-1/2} (Eq. 3.67), whose eigenvalues are √(tr ρ0E_b / tr ρ1E_b) (Eq. 3.92). Proved for invertible ρ1 with a separate support construction, in finite dimension. The fidelity is the unsquared one; Jozsa’s is its square. The thesis says nothing about trace distance, and the analogous problems for Rényi overlaps and the quantum Chernoff bound are left open. | Active |
| THEORY-585 v2 | In the Döring–Isham scheme for realising collections of systems in topoi, disjoint sums of quantum systems compose exactly; along a tensor product of finite-dimensional systems, the pull-back of a constituent’s quantity agrees with the composite’s own quantity at a context exactly when every projection in it with proper support on the first factor has the form P⊗1, so it fails for every non-scalar quantity and no operator on the composite realises the pull-back | Döring & Isham, paper IV (2007/8), LIT-310 (NOTE-285), restated in LIT-378 §§11–13 (NOTE-326). Classical physics satisfies the translation condition (3.18) exactly. For quantum disjoint sums the pull-back of δ̆(A₁⊕A₂) is δ̆(A₁) (Lemma 4.2, 4.24; checked). For H₁⊗H₂ the pull-back gives δ(Â₁)_{V_W}⊗1̂ at each context W, which equals δ(Â₁⊗1̂)_W on contexts V₁⊗ℂ1̂. That it differs elsewhere, and that no operator realises it, are asserted. The rules are “partly experimental”, and the trivial-system rule contradicts the series’ own definition of contexts. | Active |
| THEORY-586 | The ψ-ontology theorems exclude only overlap of the distributions that distinct quantum states induce over ontic states; overlap is sufficient but not necessary for reading ψ as knowledge, so a model in which the state is ψ-ontic in Harrigan and Spekkens’ sense can still have ψ represent partial knowledge | Hance, Rarity & Ladyman (2021), LIT-090, read in full in NOTE-072. The formal ψ-ontic/ψ-epistemic split is contradictory by stipulation, while the informal “ontic” and “epistemic” are not exclusive. So PBR and the related theorems bound the geometry of µ_ψ, not the interpretation of ψ. The paper proves nothing; its positive criterion (Eq. 6) is predictive incompleteness, and its Appendix A makes claims the record’s readings contradict. The defensible paraphrase of PBR is “not ψ-epistemic in the overlap sense, given preparation independence”. | Proposed |
| THEORY-587 | A U-turn stopping rule for Hamiltonian Monte Carlo leaves the target invariant once the trajectory is built as a random balanced doubling tree and the next state is drawn only from states that could have regenerated it; with a dual-averaged step size it matched the best hand-tuned identity-mass HMC on two of four test posteriors and beat it about threefold on the other two, and its ergodicity is not shown | Hoffman & Gelman (2011), LIT-085, read in full in NOTE-081. The invariance argument (conditions C.1–C.4 and the 2⁻ʲ tree probability) is complete, and so is the O(j)-memory kernel. Ergodicity is not addressed. The efficiency comparison is against HMC with an identity mass matrix on four smooth, near-unimodal targets, and the dual-averaging constants were tuned on one of the four. The account is of the 2011 algorithm; production NUTS has since changed its selection rule, U-turn criterion and adaptation. | Active |
| THEORY-588 | Lemma-based models of language production build in a lexicalist assumption, and the failure is algorithmic as well as representational: as long as retrieval of stored word-sized units and building of syntactic structure are separate stages, richer stored units cannot handle polysynthetic words, idioms whose parts syntax separates, or suppletion conditioned by an unplanned object | Krauska and Lau (2023), LIT-031, read in full in NOTE-029. A Hypothesis and Theory article with no new data and no implementation. Its diagnosis of named models (Levelt, the Consensus Model, lexically sized increments, treelets) is strong as textual analysis; the case that they fail on Inuktitut, Vietnamese collocations and Hiaki suppletion is argued from a few examples each, and Eberhard et al. are conceded to handle Hiaki in part. The 8-stage replacement model and its aphasia predictions are a verbal sketch, and this account does not rest on them. | Proposed |
| THEORY-589 | No principle of mereology is merely a fixing of what ‘part’ means: even reflexivity, transitivity and antisymmetry face counterexamples that do not rest on equivocation, and every principle beyond them is contested, so classical mereology is one substantive theory among several and not a neutral default | Varzi, SEP “Mereology”, LIT-124, read in full in NOTE-163. The entry’s verdict, reached by surveying counterexample families: Antisymmetry “can hardly be regarded as constitutive”, and most ordinary-language objections to Reflexivity and Transitivity equivocate, leaving the metaphysical ones. It is the author’s informal argument, and he is a known extensionalist who gives that side the last word on extensionality. Its headline that “all composition principles turn out to be controversial” is stronger than its own verdict that bounds for overlapping things are “rather uncontroversial”. It corrects the record’s earlier summary, which called the partial-order core uncontroversial. | Proposed |
| THEORY-590 | The self whose governance makes action autonomous is not the self whose persistence is personal identity: governance by an essence of volitional necessities would make action authentic, not autonomous; losing a defining care costs one’s grasp of who one is, not one’s existence; and wholeheartedness won by extruding a desire is a defence, not health | Velleman (2002), LIT-292, read in NOTE-268. A critique of Frankfurt’s late (1990s) view that autonomy is governance by the essential character of the will, an essence that is also the condition of one’s identity. It argues by counterexample (Winnicott’s False Self, the Agamemnon sequel), from Freud’s Rat Man, and by debunking genealogy. The positive view, that “self” marks reflexivity and that autonomous action is motivated in part by the understanding, is stated “briefly” and argued elsewhere. Frankfurt’s reply is unread. | Proposed |
| THEORY-591 | Cognition has two necessary marks, involving non-derived content and a distinctive kind of causal processing, and as a contingent fact only processes in the brain have both, so notebooks, screens and tools coupled to a thinker are not parts of cognition, and human-plus-tool systems will support no science of their own | Adams & Aizawa (2001), LIT-438, read in NOTE-368, restated against Clark in 2010, LIT-455, read in NOTE-380 from a draft. Both marks are assumed: the first on a claimed consensus, the second on how mature sciences individuate kinds. The authors grant the parity principle and that cognition could extend; the claim is that it does not. The “no science of tool use” half is offered as a bet. Rupert, the other critic, rejects the derived-content argument as question-begging. | Proposed |
| THEORY-592 | Every unital Banach *-algebra satisfying Gelfand and Naimark’s norm conditions is isometrically *-isomorphic to a norm-closed algebra of operators on a Hilbert space, built from positive functionals by what is now the GNS construction, and a commutative one is the algebra of all continuous functions on its compact maximal-ideal space | Gelfand & Naimark (1943), LIT-313, read in full in NOTE-303. Theorem 1 embeds every normed -ring in B(H) for a Hilbert space not assumed separable; Lemma 1 is the commutative case, resting on Gelfand’s 1941 paper and Šilov’s boundary. The paper never says “C-algebra” or “GNS”. It assumes two axioms it suspected redundant, and notes that a single norm identity may replace two others. It gives the object-level isomorphism R ≅ C(𝔐), not a categorical duality, and nothing on uniqueness or irreducibility of the representation. | Active |
| THEORY-593 v2 | Perceptual learning can install perceiver-specific frames that change which objects a perceiver individuates from the same input, so cognition can shape the perceptual system over time while leaving open whether any single percept is cognitively penetrated | Ivy & Mroczko-Wąsowicz (2025), LIT-099, read in NOTE-150. A conceptual proposal: a frame is installed by learning, often top-down, and then runs as a perceiver-specific structural principle of objecthood, so the system-level and episode-level questions about cognitive penetration come apart. The support is others’ results reread through the concept, and one eye-tracking study of the authors’. The paper does not say what “bottom-up” means once priors sit in early processing, calls a frame “a specific top-down prediction” in §3.iii, and shows different weightings, not different objects. | Proposed |
| THEORY-594 | Unitarily inequivalent representations in quantum field theory need not refute ontic structural realism: what does physical work in spontaneous symmetry breaking and in the DHR derivation of quantum statistics is structure across representations, so a structural realist who takes structure to be modal and to span them can accept that work, though the modal conception is undeveloped and the removal of Howard’s premise rests on Baker’s sufficient condition for intertranslatability | French (2010 draft; SHPMP 2012), LIT-170, read in NOTE-162 from the unpaginated preprint. Every technical step is imported (Wallace, Earman, Ruetsche, Halvorson & Müger, Baker); the paper’s contribution is interpretive and informal. The DHR result that statistics and charge kinds follow from the algebra is strong physics; that it favours OSR is French’s reading. The modal “trans-world” structure is proposed, not developed, and the combined third option “obviously requires further elaboration”. | Proposed |
| THEORY-595 | A filter over a set of worlds is a finitely consistent propositional theory and an ultrafilter a negation-complete one; read so, the ultrafilter extension theorem is Lindenbaum’s lemma for propositions, and Łoś’s theorem builds a model that makes true exactly what an ultrafilter says, which proves first-order compactness without proof theory, given the axiom of choice | Turner (preprint 2021, published 2025), LIT-145, read in NOTE-177. An expository paper: “None of the results are novel” (p. 2). Maximal, prime and ultra filters coincide (Thm 2); every filter extends to an ultrafilter (Thm 3); Łoś’s theorem (Thm 9); compactness (Thm 12). The results are standard and correct, though the write-up has slips. A filter is only finitely consistent, and that is the point. The pairings with Lindenbaum and Henkin are analogies, not reductions. | Active |
| THEORY-596 | To ascribe beliefs and desires is to predict a system by assuming it is rational and its beliefs mostly true, so a wholly false belief system has no coherent intentional description and contradictory beliefs no stable one, and the believer, like the person built on that notion, is an idealisation that real creatures only approximate | Dennett (1971), LIT-440, read in NOTE-350, and his reply to Stich (1980), LIT-456, read in NOTE-371. Belief ascription presupposes optimal design relative to goals, so “a false belief system is a conceptual impossibility” and, following Quine, the evidence for ascribing p is the best evidence against ascribing a contradictory q. In 1980 Dennett concedes the price: the intentional system, and the person, is “an unrealizable idealization”. Argued from the logic of ascription and from evolution by assertion; no data. It is a claim about what ascription requires, not about what is in heads. | Proposed |
| THEORY-597 | Meditation-related experiences that Western Buddhist practitioners report as challenging span 59 kinds in seven domains, from fear and sleep change to altered self-other boundaries, and they are reported in daily practice, at under an hour a day and in the first days of practice, not only on intensive retreat; the frequencies come from a sample chosen for difficulty, and the causal link is the practitioners’ own attribution | Lindahl, Fisher, Cooper, Rosen & Britton (2017), LIT-066, read in full in NOTE-036. Interviews with 60 Western Buddhist practitioners, recruited for having had a challenging meditation-related experience, and 32 teachers and clinicians were coded into 59 experience categories in seven domains. Some practitioners reported onset within ten days of starting, at under an hour a day, or in daily practice. That rebuts the claim that difficulties arise only on retreat or in the predisposed. It gives no rates and no relative risk: the sample was chosen for difficulty, and causation is self-attributed, with a causality score of 2 or more built into inclusion. | Active |
| THEORY-598 | Group interactions that enter a dynamical model linearly, as in diffusion on simplices or random walks on hypergraphs with edge-independent vertex weights, reduce to pairwise dynamics on a reweighted graph; the abrupt transitions, bistability and stabilised coexistence reported for higher-order systems come from group terms that enter nonlinearly, and whether the representation is a hypergraph or a simplicial complex is itself a modelling claim that changes the outcome | Battiston et al. (2020), LIT-091, read in full in NOTE-057. A review: the reduction results are its own §V algebra (three-body linear diffusion becomes a weighted graph Laplacian, Eq. 35) and reported results it cites (Chitra and Raphael on hypergraph walks); the nonlinear effects are one-paper summaries, mostly mean-field or all-to-all. The review never states the condition as a result, and its introduction and conclusion claim more (“no doubts”, “profoundly change”), citing linear cases among the examples. The condition is the record’s reading of what its body shows; edge-dependent vertex weights also escape the reduction. | Active |
| THEORY-599 | In trained neural-network weights stored as BF16 or FP32, nearly all the redundancy a lossless coder can remove lies in the floating-point exponent, which occupies about 40 of its 256 values and compresses to about a third under single-symbol Huffman coding, while sign and mantissa are near-incompressible; the redundancy belongs to the number format, not to the learned function | Hershcovitch et al. (2024), ZipNN, LIT-268, read in full in NOTE-241. Fifteen models broken down by byte group (Table II), with the exponent skew shown on four (Fig. 2) from 1 GB middle slices. A parameter shuffle changes Zstd’s exponent compression by at most 0.05%, so the gain is order-0. The paper never computes an entropy. Its explanation of the skew is partly wrong as stated, and its remark that the redundancy shows overparametrization unused does not follow from what it measured. | Active |
| THEORY-600 | A definition of health and disease by social justice alone cannot fix what counts as disease: with justice left undefined, a majority with other values could medicalise what the definition was meant to protect, and unless medicine is fixed from outside, the category drifts until health becomes justice | Veit (2025), LIT-098, read in NOTE-097 from the PhilSci-Archive preprint. The target is Kukla’s institutional definition: a condition is a health condition iff medicalising it would be best for collective wellbeing. The argument is informal and has two horns. One is a thought experiment (p. 14). The other rests on an asserted, undocumented premise about how medical tools evolve (p. 15). The extension from Kukla to “any purely normativist account” is asserted, not shown case by case. Veit concedes the first horn bites only without moral consensus. | Proposed |
| THEORY-601 | Among US undergraduates in the HERI surveys, students with higher verbal ability and stronger self-reported intellectual dispositions select into philosophy, and after adjusting for their entering SAT or freshman scores philosophy majors still score higher than other majors on GRE Verbal (SMD 0.48) and LSAT (0.35) but not on GRE Quantitative, and report more Habits of Mind and Pluralistic Orientation; the adjusted advantage is an association, not a shown effect of studying philosophy | Prinzing & Vazquez (2025), LIT-155, read in full in NOTE-167. HERI/CIRP freshman–senior data on 649,511 students at 804 institutions, 4,843 philosophy majors. Selection is real (SAT Verbal OR 1.57, SAT Math none). Baseline-adjusted mixed models and an IPTW check agree on the verbal and logical-test advantage and on its absence for quantitative tests. All test scores are self-reported, the SAT is an imperfect baseline for the LSAT, and nothing rules out faster verbal growth or harder test preparation among those who choose philosophy, so the paper’s causal title is not part of this account. | Active |
| THEORY-602 | An ergodic source’s entropy is the least average rate at which it can be encoded, a noisy channel has a capacity below which any rate can be sent with arbitrarily small error and above which the equivocation cannot fall below the excess, and a source can be reproduced at a given fidelity over a channel exactly when its rate for that fidelity does not exceed the capacity; Shannon rests the justification of entropy on these theorems, not on the axioms that single out −Σ p log p | Shannon (1948), LIT-764, read in NOTE-591: Parts I–II closely, Parts III–V and the later appendices skimmed for their theorem statements. The noisy-channel achievability proof is a random-coding sketch at the typical-set level, not a full ε–δ argument, and the strong converse is not proved; the theorems themselves were later made rigorous. Shannon says the uniqueness theorem for H is “in no way necessary” to the theory. The theorems assume ergodic, finite-state sources and channels and say nothing about meaning. | Active |
| THEORY-603 | In the Iowa gambling task, every one of ten controls and none of six patients with bilateral ventromedial prefrontal damage developed anticipatory skin-conductance responses, and three patients who could state the right strategy still did not switch to the good decks; the controls’ preference for the good decks became significant only once they reported a hunch, so the study does not show advantageous choice or deck-specific bodily signals before any awareness | Bechara, Damasio, Tranel & Damasio (1997), LIT-383, read in NOTE-331. The robust results are the group difference in anticipatory SCRs (Fisher’s exact, one-sided P < 0.001) and the insufficiency of stated knowledge in three patients. The abstract’s “before they realized which strategy worked best” and “before they knew” outrun notes 8 and 9: the pre-hunch choice preference was not significant, and the pre-hunch SCR effect reported is group × period, with no bad-versus-good deck test. Nothing here shows that the SCR, or what it indexes, causes the choice. | Active |
| THEORY-604 v2 | Most mathematical dualities are adjunctions between one category and the opposite of another, which become dual equivalences on their fixed points; what makes them dualities rather than equivalences is the reversal of arrows, so many of the ‘dualities’ physicists name are, in the mathematician’s sense, equivalences or symmetries | Corfield (2017), LIT-115, read in NOTE-141. A short programmatic paper. That most dualities of interest are covered by constructions around adjunction is shown by worked exposition of standard cases, not proved. There is unlikely to be “a single monolithic account” (pp. 59–60). Reserving “duality” for structural reversal is a stated preference, and the verdicts on string dualities are a paragraph each. The proposal that philosophers of physics need homotopy type theory is an expectation. | Proposed |
| THEORY-605 | In any ontological model that reproduces the quantum predictions and treats independently prepared systems as having product distributions over a joint state that is just the list of their states, distinct pure quantum states have distributions over the ontic state whose supports overlap in measure zero, so the pure state is fixed by the ontic state; approximate agreement within ε bounds the overlap by 2ε^{1/n} | Pusey, Barrett & Rudolph (2011), LIT-062, read in full in NOTE-030. For any two non-orthogonal pure states, n copies prepared independently and an entangled measurement in which each outcome is impossible for one product preparation force zero overlap; with ε error, D(µ0, µ1) ≥ 1 − 2ε^{1/n} (Eq. 7). Determinism and locality are not assumed. Preparation independence, in its strong product-space form, carries the weight, and dropping it permits ψ-epistemic models. The theorem excludes overlap, not every reading of ψ as knowledge, and it does not reach theories outside the ontological-models framework. | Active |
| THEORY-606 | If consciousness words have meaning only through what is public, an entity is a candidate for consciousness only if an encounter with it in a shared world can be engineered, at least in principle; then disembodied chat agents, even with tools and memory, are not candidates, robots and virtually embodied agents could be, and beyond what an informed community comes to say there is no further fact about their consciousness | Shanahan (2024), LIT-465, read in full in NOTE-382 from the arXiv v2 preprint. A conditional, and the condition is the paper’s method: a later-Wittgensteinian reading of consciousness language, summarised, not defended. The candidature test is stipulated and illustrated by the octopus and an imagined alien cube. The verdict on chat agents follows from it. Calling functionalism and identity theory “dualistic” is a definition, not an argument. The two passages on the self (no “self worth preserving”, no “person behind the mask”) are asserted and are not part of this account. | Proposed |
| THEORY-607 | The individuals that appear in an evolutionary transition in individuality are a summary description of lower-level processes, not a new level of fact: a partition of particles defines collectives when predicting at the coarse grain matches predicting at the fine grain across many traits, and collectives become indispensable, and so quasi-ontological, only because finite measurement and computation make the fine-grained prediction unaffordable | Bourrat (2023), LIT-049, read in full in NOTE-064. The formal criterion is accuracy only: δC = C_T − C_P < θ across many traits, conditioned on the environment where ecology could fake coherence. As written it is degenerate, since the identity partition gives δC = 0. The cost that is meant to stop that is argued separately, by a 100-operation toy, and never put into the criterion. Nothing is computed on any model. The abstract’s “cannot be dismissed as merely epistemic” is stronger than the body, which says one “pretend[s] as if” the level of selection changed. | Proposed |
| THEORY-608 | On one physical piano-movers puzzle scaled to the solver, ant groups solve better as they grow, while human groups barred from speech and gesture solve worse than individuals and talking groups only about as well as one; large ant groups keep speed and heading through wall contact, and the human mechanisms offered are fitted or observed informally, not tested | Dreyer et al. (2024), LIT-075, read in NOTE-040. Large ant groups (n = 28) reach about 90–100% success by 400 corridor widths, small groups (n = 48) about 50%. Restricted human groups do 32% worse than individuals’ median, talking groups 7% better. There are no inferential statistics. The ant persistence mechanism is supported by collision data and a model whose carrier numbers fall short of calibration; the human majority vote (greediness P = 0.2) is tuned by eye, and “follow a random leader” rests on unrecorded observation. One ant species, one puzzle, one human population. | Active |
| THEORY-609 | When implementing an automaton requires reliable, counterfactual-supporting transitions for every formal state, Putnam’s construction fails, but any system with a clock and a dial still implements every inputless finite-state automaton, and any system with the right input–output dependencies, an input memory and a dial implements every finite-state automaton with those dependencies, so finite-state automata cannot carry computational sufficiency; combinatorial-state automata are argued, not proved, to escape | Chalmers (1996), LIT-404, read in NOTE-342 from the author’s HTML copy. The failure of Putnam’s construction and the clock-and-dial and input-memory theorems are constructive proofs given the definitions, so FSA-functionalism “still almost reduces to behaviorism”. That a combinatorial-state automaton can be implemented only by the right fine-grained causal structure is a sketch: the obvious blind construction grows by a factor of n per step, and that every construction does is asserted. Logically possible false implementations and the one-region-per-component condition are left open by the author. | Active |
| THEORY-610 | What survives radical theory change in a mature science, and so what its predictive success warrants belief in, is mathematical structure, equations carried over intact or recovered as limiting cases, and not the ontology that interpreted them, as Fresnel’s reflection and refraction equations survive into Maxwell’s theory while the elastic-solid ether does not | Worrall (1989), LIT-315, read in NOTE-297. Epistemic structural realism, credited to Poincaré, offered as the one position that keeps both the no-miracles argument and the pessimistic induction. The support is one worked case, which Worrall himself calls unrepresentative because the equations survive intact, and an appeal to the correspondence principle with one further example. “Structure” and “structural approximation” are undefined. The view is agnostic about what there is; the ontic turn, Ramsey sentences and the Newman objection belong to later work. | Proposed |
| THEORY-611 v2 | Classifier-free guidance extrapolates between a conditional and an unconditional score learned by one network; with exact scores this equals classifier guidance by the classifier the generative model defines through Bayes’ rule, but learned scores need not be conservative, so the guided field is in general the gradient of no density and the tilted distribution that motivates guidance is not shown to be what is sampled | Ho & Salimans (2022), LIT-839, read in full in NOTE-603, with the derivations of Section 3 checked line by line. The non-conservativeness argument is credited to Salimans & Ho (2021). The FID–IS trade-off is shown on class-conditional ImageNet only. NOTE-603 declined a THEORY because the anthology holds the account of what the guidance weight does to metrics; this one states only the probabilistic point, which the record’s CLAIM-123 uses. | Active |
| THEORY-612 | Natural selection cannot be both a cause and an effect of a process such as niche construction: if selection is an emergent population-level process, niche construction partly composes it, and a whole and its parts are not independently fixable and so not causally related; if selection is not emergent, it is either no cause at all or incoherently individual-level. Niche construction can still cause the product of selection | Hazelwood (2023), LIT-156, read in full in NOTE-137. A dilemma against strong reciprocal causation in the extended evolutionary synthesis, aimed at Laland and colleagues. Emergence is Wilson’s synchronic dependence plus autonomy, cashed out as composition; causation is Woodward’s interventionism with independent fixability. Its force rests on a process/product split for selection and a compositional reading of realization, both defended by citation and flagged as contestable, and its second horn considers only two non-emergent options. The weak sense, that organisms and environments affect each other, is granted as unobjectionable. | Proposed |
| THEORY-613 | The Moral Foundations Questionnaire-2’s six factors, Care, Equality, Proportionality, Loyalty, Authority and Purity, fit across 19 nations, Equality and Proportionality are nearly uncorrelated in WEIRD nations, and the US split between individualizing and binding foundations appears in only three national networks | Atari, Haidt, Graham, Koleva, Stevens & Dehghani (2023), LIT-500, read in NOTE-398. 36 items, developed in 25 populations, fit six factors in 19 nations (ESEM CFI .979). Equality and Proportionality correlate .21 on average, from .47 to −.04. Purity alone fails intercept invariance, and it carries the headline that Purity is the least WEIRD foundation. The samples are online and about 200 per nation. | Proposed |
| THEORY-614 v2 | If pretraining text is a mixture of hidden Markov models indexed by a latent concept and a model fits that distribution exactly, then a prompt of concatenated examples moves the posterior onto the prompt’s concept, and the in-context predictor becomes Bayes-optimal as examples accumulate, whenever each example’s evidence for the concept outweighs the cost of the improbable transitions between examples; whether trained networks learn in context this way is not shown | Xie, Raghunathan, Liang & Ma (2021), LIT-797, read in NOTE-633. Theorem 1 is proved under Assumptions 1–5 and a distinguishability condition; Theorems 2–3 give roughly 1/k excess risk without it. The proofs were not followed in the reading. NOTE-633 declined a THEORY because the result is conditional on exact fit to a specific generative model, so it is a consequence of that model, not a fact about language models. It is filed Proposed under the owner’s ruling, with the condition in the title. | Proposed |
| THEORY-615 | Stubborn distrust of scientific experts can follow validly from the truster’s position: one with little say in collective decisions, who has reason to think the experts’ service ethos leaves out their core interests, has a reason to distrust an expert because of the expert’s prestige, whatever the expert’s competence or goodwill | Desmond (2022), LIT-158, read in NOTE-113. A “how-possibly” argument, not a demonstration: a five-step scheme (§6, pp. 16–17) from status vulnerability and service doubt to distrust “in virtue of” prestige. The paper says it shows validity only. It leaves open whether the premises ever hold in a liberal democracy, gives no data linking status to distrust, and does not compare its account with testimonial injustice or the empirical predictors of conspiracy belief. The abstract’s “justifiably” claims more than the body. | Proposed |
| THEORY-616 v2 | If a system has beliefs and desires just when attributing them, with rationality, predicts its behaviour well enough against rival theories, then the bearer of a language model’s attitudes is the instance created by one context, not the model, the case that instances have them is presumptive and rests on tractability, and the best current desire hypothesis is helpfulness, honesty and harmlessness plus intrinsic desires a prompt installs | Goldstein & Lederman (2025), LIT-206, read in NOTE-138 from the preprint. Conditional on objective interpretationism, which the authors do not defend. The instance thesis is moderately argued; the presumptive case for attitudes rests on a tractability comparison never operationalised or measured; HHH+0 is “provisional”, and its discriminating test is a conjecture. All the empirical support is second-hand and qualitative. | Proposed |
| THEORY-617 | In additive Gaussian noise independent of an input of finite power whose law does not depend on the signal-to-noise ratio, the derivative of mutual information with respect to that ratio is half the minimum mean-square error of the optimal noncausal estimator, so mutual information is accumulated estimation error over SNR; in continuous time the causal filtering error equals the noncausal error averaged over SNR, and the identity fails with feedback | Guo, Shamai & Verdú (2004), LIT-058, read in full in NOTE-086. Proved five ways for every finite-power input, in scalar, vector, discrete-time and continuous-time forms. It concerns the optimal, conditional-mean estimator; carrying it to a trained diffusion model’s learned denoiser needs the mismatched version, which is later work. Theorems 3, 4 and 11 are stated without proof. | Active |
| THEORY-618 | Neural circuits that must represent hierarchically organised states in few dimensions use a hyperbolic geometry, three-dimensional where it has been measured, because hyperbolic space holds exponentially many well-separated states within a small radius; the argument from Zipf’s law to this geometry does not hold, and the evidence is two Betti-curve studies tested only against uniform Euclidean nulls | Sharpee (2019), LIT-875, read in NOTE-670: a four-page programmatic review with no new result, whose reading filed no THEORY because its claims are conjectures. Filed here as Proposed because the record holds two tests of the conjecture, odour statistics (LIT-872, THEORY-191) and CA1 place-cell correlations (LIT-876, THEORY-192), and no general statement. The Zipf step shows a shared exponential count of states, which any system with extensive entropy has, not a shared metric, and the rigidity argument for three dimensions cites Mostow’s theorem, which concerns finite-volume manifolds and says nothing about noisy point clouds. | Proposed |
| THEORY-619 | Over the poset of commutative von Neumann subalgebras, coarse-graining a projector to a smaller subalgebra is exactly the direct image of its clopen region of the Gelfand spectrum under restriction, so the coarse-graining presheaf is the presheaf of clopen spectral regions; and a quantum state’s sieve-valued truth values are fixed by one coherent family of regions, its supports: a proposition is true at a subcontext exactly when the support there lies under the coarse-grained proposition | Butterfield & Isham (2001), “Topos Perspective on the Kochen-Specker Theorem: IV”, LIT-382, read in full in NOTE-328. §2.4 proves G ≅ CloΣ: restricting the characters of V₁ that make P̂ true gives exactly the characters of V₂ that make its coarse-graining true, via a cited state-extension theorem. Theorem 3.1 shows that any assignment defined by “support ≤ coarse-grained proposition”, with supports forming a global element of G, is a sieve-valued valuation obeying FUNC; a state’s supports qualify. Both theorems are close to definitional. Nothing here builds Heyting operations on clopen sub-objects. | Active |
| THEORY-620 | Walsh’s 1923 functions are a closed orthonormal set on (0, 1) of ±1-valued step functions, each a parity of finitely many binary digits, whose expansions behave like Fourier series: grouped uniform convergence for continuous functions, convergence under bounded variation, localisation, Cesàro summability, and divergence at any chosen point for some continuous function | Walsh (1923), LIT-300, read in full in NOTE-281, with the explicit formula and the Lebesgue-constant recurrence checked for small n. Closure is inherited from Haar’s system, to which Walsh’s is related by an orthogonal change of basis within each dyadic level. Theorems II–X give the Fourier-like convergence theory. The paper never mentions groups or characters: that these functions are the characters of the Cantor group, and of the Boolean cube on n digits, is a later identification. | Active |
| THEORY-621 | Indexing each quantum fact to the system it is a fact for, and computing probabilities only between facts relative to the same system, removes the contradiction between the collapse and unitary probability rules in Wigner’s-friend cases; the price is that values are not held at all times or by all systems alike, there is no global view, and no quantum state of the universe | Rovelli (2021), LIT-177, read in full in NOTE-174. For a fact a and exclusive facts bᵢ, the collapse rule Σᵢ|W(c,bᵢ)|²|W(bᵢ,a)|² and the unitary rule |Σᵢ W(c,bᵢ)W(bᵢ,a)|² differ by interference; RQM applies the first only when the bᵢ and c are relative to the same system. Decoherence makes some relative facts stable. The core rule is postulated, not derived, and inter-observer consistency gets one sentence. The chapter is expository, and several of its headline claims outrun its support. | Proposed |
| THEORY-622 | Spatial boundaries are bona fide where a spatial discontinuity or a heterogeneity of material is present and fiat where they exist only by demarcation; the two obey different topologies, distinct bodies are never in bona fide contact, so any whole of separate bodies is a fiat object, and real properties of the material still enable and constrain where fiat boundaries can be drawn | Smith & Varzi (2000), LIT-1024, read in full in NOTE-721. A typology with a formal sketch: ordinary closure topology for bona fide boundaries, and a Brentanian theory of coinciding boundaries for fiat ones, which are parts of what they bound. The test is whether a discontinuity is there, not who or what made it. The theory is spatial, synchronic and pitched at the common-sense level; it has no models or consistency result, and the typology is stipulated by examples. It does not map onto the record’s produced/imposed distinction, and it classifies the record’s combined forms as fiat without choosing among them. | Proposed |
| THEORY-623 | In the two tests of contextuality in language data that the record has read, the contextuality is put there by the experimenter or not secured: meaning-selection models of ambiguous phrases estimated from corpora are all signalling and their two Contextuality-by-Default verdicts are plausibly noncontextual by their own bootstrap, while BERT’s 52 million anaphora models have a support fixed by the sentence schema, so whether each counts as contextual depends only on how uncertain the model’s three referent choices are | Lo, Sadrzadeh & Mansfield (2024), LIT-844, read in NOTE-648, and Wang, Sadrzadeh, Abramsky & Cervantes (2021), LIT-842, read in NOTE-645. Both readings recomputed the criteria. That 71.1% CbD-contextual measures BERT’s uncertainty is NOTE-648’s derivation from the stipulated support (CNT1 = 2 − Δ). The only possibilistically contextual phrase model has hand-set supports. Neither study uses human judgements, so neither bears on whether people’s interpretations are contextual. | Active |
| THEORY-624 v2 | Orseau, McGill and Legg cast whether an identified system is an agent or a device as Bayesian model comparison between descriptions of the function it optimises and descriptions of its input-output mapping, so that the verdict is relative to the observer’s prior; on seven toy gridworld trajectories goal-seeking comes out agent-like and wall-following device-like, and they argue that under a speed prior everything may look like an agent | Orseau, McGill & Legg (2018), LIT-911, read in NOTE-705. A formal version of Dennett’s choice of stance: the posterior probability that a system is an agent, from mixtures of goal-optimizing (inverse RL) and input-output descriptions. Illustrated on seven gridworld trajectories, with no human study. It presupposes an identified system, and its verdicts depend on the prior; under the speed prior everything may look like an agent. | Active |
| THEORY-625 v2 | Institutional facts are status functions, imposed by collective acceptance on things that cannot perform the function by their physical structure alone; the status carries deontic powers that give desire-independent reasons for action, and it exists only as represented, so institutions require language; ‘X counts as Y in C’ is the common case of the more general ‘We accept (S has power (S does A))‘ | Searle (2006), LIT-482, read in NOTE-388 in its Papers printing, the record’s readable statement of The Construction of Social Reality (LIT-485, unread). Conceptual analysis, not argument: the three primitives are asserted to suffice, collective intentionality is referred to an unread 1990 paper, and the animal line is hedged. The paper revises the book: some Y terms have no X, and the general form is “We accept (S has power (S does A))”. Hindriks & Guala’s rules-in-equilibrium account is its rival on what a constitutive rule adds. | Proposed |
| THEORY-626 | Moral judgments are made relative to the social relationship an act is taken to occur within: each of four relational models (communal sharing, authority ranking, equality matching, market pricing) carries a moral motive (Unity, Hierarchy, Equality, Proportionality), so the same act can be required under one and wrong under another | Rai & Fiske (2011), LIT-507, read in NOTE-405. A theoretical review with no new data. Its strongest support is cited work on relational framing and on morally motivated violence. Which model is in force is read off after the fact, so the central claim risks being unfalsifiable as stated. Purity and ingroup loyalty are assigned to one motive, Unity, by argument. | Proposed |
| THEORY-627 | A nudge discovered by a learning system, unlike one a person designed, comes with no prior theory of why it works and may exploit a cognitive process no theory yet describes, so judging it by its outcomes cannot diagnose or repair its side effects; overseeing it needs inspection of which human processes it exploits, by people expert in human cognition | Schmauder et al. (2023), LIT-179, read in NOTE-171. An argument by analogy from Hausman’s reply to Friedman: a test drive is not enough if you must repair the car. Its evidence is reported from others: an RL agent moved choices of a target lottery from 50% to 70% by exploiting documented biases (Dezfouli et al. 2020), and AI advisers learned dishonest advice against simulated clients. No case of an undocumented bias is given; that is the paper’s conjecture, and its oversight proposal is unspecified. | Proposed |
| THEORY-628 v2 | Self-production alone gives a system only an all-or-nothing norm, to go on or to die, and that distinction is available to an observer, not to the system; a graded norm the system itself has, by which viable states are better or worse for it, needs adaptivity, a further capacity to detect tendencies toward the boundary of its viability and to act so as to reverse them, and sense-making and agency need adaptivity | Di Paolo (2005), LIT-1017, read in full in NOTE-719. A conceptual argument against Weber and Varela: autopoiesis in its original formulation entails conservation, not active homeostasis, so a bacterium whose intake is below consumption does not seek food “just because” it is autopoietic, and balancing at a cliff edge and falling over it both conserve autopoiesis. Adaptivity is defined, graded and recursive; pathology becomes failure of adaptivity while autopoiesis continues. There is no formal model, and the viability set is defined in one sentence. Proposed. | Proposed |
| THEORY-629 | Every continuous linear functional on a Hilbert space is the inner product with a unique vector of the same norm, given in any orthonormal basis by the conjugated values of the functional on the basis; completeness is what makes it so, and Riesz’s 1907 statement on L² asserted only that a representing function exists | Adler (2021), LIT-243, read in full in NOTE-854: two complete proofs, by projection (Thm 3.5) and by an orthonormal basis (Thm 4.9), with completeness used once, in the projection theorem. Riesz (1907), LIT-326, read in NOTE-289, is the priority note: existence of k with U(f) = ∫ f k for continuous linear U on square-summable functions, stated without proof, uniqueness or norm. The theorem says nothing about kernels, factorisation or uniqueness of representations. Both readings advise citing a textbook for anything leaned on. | Active |
| THEORY-630 | A protective measurement yields the expectation value ⟨A⟩ on a single system in the ideal limit, and with enough observables ψ up to a global phase; this shows ψ to be ontic only if the protection procedure carries no information about ψ, a premise that Zeno and adiabatic protection, which select ψ from a discrete eigenbasis the experimenter chose, do not meet | Gao (2016), LIT-121, read in full in NOTE-140. Under Zeno protection the pointer shifts by exactly ⟨A⟩ with no entanglement (eqs. 1.9–1.13), and projectors on regions plus a current operator give ρ and j (eqs. 1.14–1.16). Gao argues three routes from this to ψ-ontology, claimed to need no preparation independence. All three rest on the premise that the protection does not “know” ψ, which Gao’s own fn. 10 partly concedes is false. The random-discontinuous-motion ontology and the collapse model built on it are further, weaker steps. | Proposed |
| THEORY-631 | Standard unitary quantum theory and the general quantum theory of open systems are intertranslatable on their common domain, so neither dependence nor justification ranks them; the open theory comes out more fundamental only through premises about interpretation, that orthodox and Everettian readings exhaust the complete readings of the state vector, and that density operators precede state vectors in how states are assigned | Cuffaro & Hartmann (2021), LIT-037, read in full in NOTE-077. Stinespring dilation one way and dropping Lindblad terms the other make the two frameworks a tie on ontic dependence (OntFund-1) and on justification (EpFund-1). The verdict for the open theory comes from OntFund-2, which holds only if orthodox and Everettian readings are all that count, and from EpFund-2, which rests on imperfect preparation. Explanatory fundamentality is effectively abandoned. The paper proves nothing formal, and its “tout court” conclusion outruns §4. | Proposed |
| THEORY-632 | Purity is moralized in self-report: in morality-as-cooperation’s own questionnaire studies, purity items are rated about as morally relevant as loyalty and authority items, and harmless purity violations are condemned, so that theory’s prediction that non-cooperative behaviour is morally neutral fails unless purity is itself cooperative | Curry, Jones Chesters & Van Lissa (2019), LIT-496, read in NOTE-412, against the prediction stated in Curry (2016), LIT-503 (NOTE-408), with the harmless-wrongs studies Haidt (2001) reports, LIT-511 (NOTE-403). In two samples, MFQ purity items are rated morally relevant at the level of ingroup and authority items, and the authors concede this “appear[s] to contradict” the theory. It is self-report from people asked about purity, not a blind count of what societies moralize, and it does not say whether purity is cooperative. | Active |
| THEORY-633 | Experiences have no phenomenal properties: introspection represents physical, quasi-phenomenal properties of sensory states as phenomenal, so what needs explaining is why experiences seem to have phenomenal properties, not how a brain produces them; a weaker view that keeps a deflated phenomenal residue is unstable unless it can say what that residue is | Frankish (2016), LIT-458, read in NOTE-384, names the view and the “illusion problem”; Dennett’s reply to Chalmers (1996), LIT-397 (NOTE-346), gives its earlier form, that subtracting every function from one’s consciousness leaves only a conviction; Frankish (2025), LIT-103 (NOTE-143), applies it to valence. A research programme, not a theory: Frankish proposes no mechanism, the instability of weak illusionism is argued by challenge, the case is abductive, and Dennett’s subtraction is an introspective assertion. It keeps consciousness in an inclusive, functional sense and denies only phenomenal properties. | Proposed |
| THEORY-634 | In a ring of M chemotactic catalyst species, each making the next one’s substrate, the non-reciprocal nearest-neighbour coupling makes the linear stability matrix circulant: the uniform state goes unstable for any M exactly when the species attract themselves, and the parity of M then decides the leading mode, a real alternating mode for even M that sorts species by parity into two static clusters, and a complex pair for odd M that can give persistent oscillation | Ouazan-Reboul, Agudo-Canalejo & Golestanian (2023), LIT-036, read in NOTE-079. The spectrum is exact for equal parameters (Eq. 5): instability iff μ(p) − μ(s) < 0, real leading eigenvalue for M = 2K, complex pair for M = 2K + 1. Brownian dynamics at M = 5 and 6 bear out the linear predictions; the odd-cycle oscillation is one trajectory at one parameter set. Direct metabolic partners repel; same-parity second neighbours co-aggregate. The origin-of-life reading is untested, and the authors concede in the review file that real catalysts’ mobilities are unknown. | Active |
| THEORY-635 | If the quantum state of a Bohmian system is identified with the velocity dispositions it induces on the particles, inequivalent states can share one dispositional history: every energy eigenstate of a free particle in a box induces zero velocity everywhere, so the reading erases differences of energy and of typicality unless the map from states to velocity fields is injective for generic solutions, which is conjectured, not proved | Belot (2011), LIT-100, read in full in NOTE-110. Under the guidance law ψ(t) gives a vector field X_t on configuration space, read as a holistic disposition. For a particle in [0,1], each φn(x) = sin(πnx) gives zero velocity everywhere, so infinitely many energy eigenstates share one dispositional history, and the distinction between φ1 and φ2 in energy and typicality is lost. The rescue rests on Goldstein’s unproved genericity conjecture (fn. 41), and the problem arises only for closed systems (fn. 42). It is a counterexample to one reading, not a verdict on ψ’s category. | Active |
| THEORY-636 | In vignette studies of US online participants, judgements that an outcome happened because the agent wanted it move with judgements that it was done intentionally when luck is manipulated, and predict them better than know-how or probability-raising do; but they account for only about half of the luck effect, and in one morally neutral case the two come apart | Quillien (2026), LIT-132, read in NOTE-092. Three Prolific studies (N = 198, 673, 142; ratings 1–7). Causation is the strongest predictor of intentionality (standardized β .46, .56, .53, against know-how .33, .20, .27 and probability-raising .14, .16, .10), and a pre-registered Knowledge × Process interaction predicted by the causal account holds (F(1, 423) = 32). The evidence is correlational, the mediation exploratory and partial (64%, 45%, 49%), and in the neutral Kraemer vignette causation shows no effect where intentionality does. The “model” is verbal; robustness is never measured. | Active |
| THEORY-637 | Treating openness in science as the unlimited sharing of research objects, with transparency ranked before reproducibility and inclusion, can narrow the epistemic diversity of research and entrench epistemic injustice, and this lowers the reliability of what is learned, so sharing is neither a necessary starting point nor a sufficient condition for reliable open science | Leonelli (2023), LIT-189, read in NOTE-098. An openly normative argument from four illustrative cases (GISAID, software stigma, crop-data linkage, the reproducibility debate) and the author’s earlier qualitative work. That sharing-first open science can reduce diversity and worsen injustice is moderately supported; that this degrades reliability is argued, not measured. The positive proposal, openness as judicious connection, gives no decision rule, and the critique targets an ideal type the author admits many initiatives do not fit. | Proposed |
| THEORY-638 | Instantiating a formal program is never by itself sufficient for understanding or intentionality, since a person can carry out a program for answering questions in Chinese by hand without understanding Chinese; whatever thinks does so in virtue of causal powers at least equivalent to the brain’s, and the reply that the whole system understands is answered only by an asserted internalisation | Searle (1980), LIT-400, read in NOTE-349 (target article only). The room is a full implementation run by a person, and his first-person verdict is read as the system’s. The decisive step against the systems reply (“the system is just a part of him”) is asserted, not shown, and which causal powers matter is left empirical. The argument is about understanding and intentionality, not consciousness, and it grants that machines, including artifacts with the brain’s causal powers, could think. Proposed; Dennett’s intentional strategy is its rival. | Proposed |
| THEORY-639 | Inductive risk arises not only when a hypothesis is accepted but in choosing a significance level, in characterising data and in interpreting results: in the dioxin cancer studies each of these choices traded false positives against false negatives, three panels scored the same rat-liver slides differently, and threshold and no-threshold readings of the same data underlie regulatory limits about 100 times apart | Douglas (2000), LIT-139, read in NOTE-145. Three worked cases from one domain, dioxin toxicology and its regulation, on secondary data (EPA 1994; Kociba et al. 1978; Goodman & Sauer 1992). The structural point and the variation in slide scoring are strongly supported. The 100-fold figure is cited from Finkel (1988) and Greenlee et al. (1991). This is the descriptive half of the paper; the claim that values are therefore required is THEORY-442. | Active |
| THEORY-640 | Measured as mutual 10-nearest-neighbour overlap, competent vision models agree more with one another and better language models agree more with vision models, but the cross-modal score reaches only 0.16 of a possible 1, is the maximum over all layer pairs, and was adopted after a global kernel metric showed only a very weak trend | Huh, Cheung, Wang & Isola (2024), LIT-302, read in NOTE-286. Across 78 vision models, those solving more VTAB tasks agree more in mutual k-nearest-neighbour structure; language models with lower bits-per-byte agree more with vision models on 1,024 image–caption pairs. The cross-modal score “only reaches 0.16” of 1, is maximised over layer pairs, and the metric was chosen after CKA “revealed a very weak trend”. It is local neighbourhood agreement that rises with competence, not kernel equality and not convergence to a model of reality. | Active |
| THEORY-641 v2 | Under a well-specified, identifiable parametric Markov model of the target given the joint past, with ergodic lagged states, transfer entropy is the limit of the normalised log-likelihood ratio for the null of no dependence on the source’s past, so it is Granger-sense predictive improvement; for finite-state chains the plug-in estimator is exactly that statistic, and under the null and the usual regularity it is asymptotically χ² with the difference in parameter counts as degrees of freedom | Barnett & Bossomaier (2012), LIT-048, read in full in NOTE-053. The consistency result is a one-line consequence of Props. 1–2, and Prop. 2 is argued informally. The χ² null is imported from Wald (1943), whose regularity conditions are not checked. The non-central χ² for T > 0 is at best a local-alternative approximation. The finite-state identity and the Gaussian equivalence (half the Granger statistic) are exact. | Active |
| THEORY-642 | Basic two-level type theory, an inner homotopy type theory with an outer level of strict equality, is conservative over homotopy type theory, so an inner type it proves inhabited is already inhabited in HoTT, but a fibrant-replacement type former would force uniqueness of identity proofs on the inner level | Annenkov, Capriotti, Kraus & Sattler (2017; MSCS 2023), LIT-095, whose §§1–3 were read in full in NOTE-047, the reading of the nLab page it supersedes (LIT-040). Props 2.18–2.19 prove that inhabitation of inner types is reflected, through a presheaf model over any model of HoTT. Thm 2.20 proves that a fibrant-replacement former implies UIP for inner types. The conservativity is the weak, inhabitation-reflecting kind. Results that use the axioms relating the two levels’ natural numbers, which untruncated semisimplicial types need, are not known to transfer. | Active |
| THEORY-643 | The restrictions on syntax reaching into words that a separate word-formation component was credited with are restrictions on heads versus phrases and on what individual affixes select, and phrases feed word formation, so a single combinatorial component can build both words and phrases | Bruening (2018), LIT-071, read in full in NOTE-065. Phrases feed English word formation productively, ellipsis and focus reach sub-word units, and claimed differences of principle (locality, adjuncts, headedness, idiosyncrasy) fail; extraction, coordination and the no-phrase constraint are restated over X0 vs XP and affix selection, with no mention of “word”. The English evidence of §§2–3 is the strong part. Several sub-arguments are provisional by the author’s own account, and Müller’s reply in the same volume disputes extraction, coordination and the resultative argument. | Proposed |
| THEORY-644 | Panpsychism escapes dualism’s problem of mental causation only in its constitutive Russellian form, where micro-experiences constitute macro-experience; that form meets three combination problems, of subjects, qualities and structure, and every response that avoids combining (emergent, autonomous or identity panpsychism) gives back the advantage in mental causation or revised physics, while the combinatorial responses remain unworked | Chalmers (2016/2017), LIT-395, read in full in NOTE-358 from the April 2015 draft. A map of the problem, not a solution or an impossibility proof, and the author says so. The dilemma is argued case by case; the strongest arguments against constitutive panpsychism, subject-summing and structural mismatch, rest on conceivability premises and on a structure-preservation principle called plausible, not shown. The verdicts on which responses are most promising are judgements of promise. | Proposed |
| THEORY-645 | A countable discrete abelian group and a compact second-countable abelian group can each be recovered as the character group of the other, and a locally compact, connected, second-countable abelian group is a compact group plus ℝʳ; Pontryagin’s 1934 paper does not prove duality for general locally compact abelian groups | Pontryagin (1934), LIT-333, read in full in NOTE-284. Theorem 5 and the First Fundamental Theorem give the duality between countable discrete and compact second-countable abelian groups, with characters valued in ℝ/ℤ. The compact half rests on Peter–Weyl with Haar measure, used to extract one-dimensional characters. The Second and Third Fundamental Theorems are structure theorems, not duality. Commutative only; for non-abelian groups the relevant object is Peter–Weyl, and characters are traces, not homomorphisms. General locally compact duality is van Kampen’s (1935). | Active |
| THEORY-646 | Skepticism about inner mental representations does not motivate fictionalism about folk psychology, because realism about beliefs as internal, intentional, causal states does not require the representational theory of mind; and a fictionalist who lets pretence yield genuine assertions about the overall state that causes behaviour is committed to that state | Drayson (2025), LIT-112, read in NOTE-117, against Toon’s Mind As Metaphor (2023). Toon’s negative argument needs “committed to internal, intentional, causal attitudes ⇒ committed to RTM”, which non-representational functionalism (Lewis, Putnam, Loar) makes false; and his metasemantic case against inner representation mistakes one motivation for RTM for part of it. His positive argument faces a dilemma: a merely behavioural overall state gives fictionalism no causal advantage, and a causal one is a reason to identify it with the belief. It argues against two motivations, assumes fictionalism coherent, and sketches the functionalist alternative by citation in one paragraph. | Proposed |
| THEORY-647 v2 | If outright belief is credence ultraclose to 1 relative to a context level, conjunction holds for any standard (‘few’) number of believed propositions and fails for an ultralarge number, which dissolves the Lottery Paradox as an accumulation of negligible rounding errors | Wenmackers (2011), LIT-163, chapter 3, read in NOTE-139. Stratified Belief, B(x) iff P(x) ≃_V 1 in Hrbacek’s relative analysis, satisfies a Stratified Conjunction Principle for a standard number of conjuncts (proved) and fails for an ultralarge number. The proofs hold inside the framework. That belief works this way is argued: any explicit threshold collapses the model back to the Lockean one, the author calls it “crude”, and knowledge is set aside. | Proposed |
| THEORY-648 | A social fact is a way of acting, thinking or feeling that exists outside individual consciousness and can constrain the individual from outside, shown by sanction or by the resistance it offers to violation; such a fact is general in a group because it is collective, not collective because general, so the group is its substrate | Durkheim (1894; book 1895), chapter I of Les Règles de la méthode sociologique, LIT-484, read in French in NOTE-391. A definition argued from examples, which its author calls “un simple résumé des données immédiates de l’observation” (n. 3). Its two load-bearing steps are asserted: that what is neither organic nor individual-psychic must have society as its substrate, and that constraint is present even where no one feels it. It is a claim about the object of sociology, not a group-mind thesis. | Proposed |
| THEORY-649 | When agents holding uniformly random consistent theories over two or three atomic sentences each average their theories once, bit by bit, with all peers within a Hamming bound of confidence, an individual agent ends up with the inconsistent theory at most 1.81% of the time, but the chance that some agent in the group does reaches 6.4% for two sentences and 16.9% for three | Wenmackers (2011), LIT-163, chapter 5, read in NOTE-139. An exact count, extended by sampling, of how often one round of bounded-confidence averaging over theories yields the inconsistent theory. The per-agent fraction F_AG peaks at 1.8112% (M = 2) and 0.3215% (M = 3); the per-profile fraction F_OP reaches 6.4298% and 16.867%. The thesis’s headline, that the risk “can be made arbitrarily small” by adding sentences, rests on two values of M and is contradicted for F_OP. | Active |
| THEORY-650 | Whether a self at one time is the same as a self at another has an answer only relative to a level of abstraction fixed by the purpose of asking, and asked at no such level it has none; the question with a substantive answer is what makes a self one thing at a time | Floridi (2011), LIT-136, read in NOTE-130. The deflation of diachronic identity is an informal argument from examples that rests on the method of levels of abstraction, assumed from elsewhere; that this “is not relativism” is one sentence, and that individuation comes before identification is asserted. It is not, as its title suggests, a criterion of personal identity, and its positive answer to the synchronic question, the three-membranes model, is “somewhat figurative” by its author’s word. | Proposed |
| THEORY-651 v2 | Disinformation incidents labelled with DISARM techniques can be carried in standard STIX 2.1 without extending it, as an intrusion set that uses attack patterns, is attributed to a threat actor and targets locations; the DISINFOX mapping that moved 118 incidents into OpenCTI this way keeps only a name, a free-text description, a first-seen date and labels beside those three relationships, with no object or property for an incident’s narratives, channels, evidence or countermeasures or for the confidence of its attribution | Sánchez González et al. (2025), LIT-083, an unreviewed preprint read in NOTE-028. The mapping is explicit (four STIX object types, three relationship types) and was exercised end to end on 118 incidents; the reading rates that demonstration strong. Nothing beyond ingestion was measured. Attribution is one ungraded edge to an actor, typically a nation-state, which is the layer the EEAS’s Exposure Matrix grades in four tiers. What the mapping is, and that the incidents were ingested, is held; whether the representation survives exchange and whether sharing helps is THEORY-1238’s question. | Active |
| THEORY-652 | Over any field, a finite-dimensional associative algebra with no nilpotent two-sided ideal is uniquely a direct sum of simple algebras, and each simple algebra is a full matrix algebra over a division algebra, which over the reals can be the complex numbers or the quaternions | Wedderburn (1908), LIT-309, read in full in NOTE-280. Thm 17 with Thm 10 gives the unique decomposition into simple algebras; Thms 20–22 build n² matrix units from primitive idempotents and give simple = primitive × full matrix algebra. Primitive here means one idempotent, which makes the factor a division algebra once semisimple (Thm 15). The field is arbitrary, which was the paper’s novelty. That the centre is spanned by the block identities follows from Thm 23’s corollary; the paper never says “centre”. The general splitting of an algebra into nilpotent plus semisimple parts is claimed in the summary but proved only in special cases. | Active |
| THEORY-653 | In the ethnographic record of the 60-society HRAF Probability Sample, seven cooperative behaviours are described as good in 961 of 962 valenced mentions, but each is recorded in between 90% and 15% of the societies, and the coding could barely have registered a negative | Curry, Mullins & Whitehouse (2019), LIT-047, read in NOTE-034. Coding eHRAF paragraphs on the 60 Probability Sample societies found 962 morally valenced mentions of helping kin, helping one’s group, reciprocating, bravery, deference, dividing disputed resources and respecting possession; 961 were positive. Presence ran from property (54/60) to fairness (9/60) and tracked ethnographic coverage (r = .43). The behaviours are defined in virtue terms and conflicts were set aside, so a negative was nearly impossible to code. It is a description of the coded record, not a test of whether morality is only about cooperation. | Active |
| THEORY-654 | For full-state linear-quadratic regulation of a single-input plant, the return-difference identity keeps the sensitivity at or below 1 at every frequency, so the loop tolerates any gain increase, a gain cut to one half and at least 60° of phase error for any Q ≥ 0 and r > 0; the guarantee does not carry over when the state is replaced by an observer’s estimate | Başar, Meyn & Perkins (2020), LIT-051, graduate course notes read in full in NOTE-062, with every worked example recomputed. §10.6 derives |1 + L(jω)|² = 1 + |P(jω)|²/r ≥ 1 for the full-state loop, hence |S| ≤ 1 and the classical margins. The derivation is for one input; the multi-input version needs more, which the notes do not discuss. The Pendubot thread shows a controllable, observable plant whose one-sensor observer-based design has gain margin below 10⁻². The result is Kalman’s and standard; the notes are an adequate free citation for it. | Active |
| THEORY-655 v3 | Social behaviour evolves as if each individual valued a neighbour’s fitness against its own by their coefficient of relationship, and its discriminations evolve to make that coefficient determinate; so kin are favoured and strangers met with hostility, relatives fight less, and haplodiploid sisters, related by 3/4, are predisposed to worker altruism | Hamilton (1964), Part II, LIT-506, read in full in NOTE-410, on Part I’s model (LIT-497). Two general principles, offered as an “unrigorous” generalization, are applied to alarm calls, kin recognition in gulls and terns, clones and colonies, Hymenoptera, and fights. The evidence is anecdotal. The author calls his positive indications for distant relatives “rather few and feeble”, reports Australian halictines and multiple mating as running against the hymenopteran hypothesis, and explains anomalies case by case. | Proposed |
| THEORY-656 | A single holistic power of the universe’s configuration, carried by bare matter points, cannot ground a subsystem’s effective wave function without changing the ontology, because the masses in a decoupled subsystem’s Hamiltonian must belong to that subsystem’s particles; dispositions intrinsic to particles or events need no such change | Dorato (2015), LIT-176, read in full in NOTE-105. Against Esfeld et al.’s holistic dispositionalism: when a subsystem effectively decouples, its Hamiltonian’s masses must be intrinsic dispositions of its particles, so the holistic view must alter its ontology between the universal and the effective wave function (pp. 14–15). The argument is moderate and posed partly as questions. The paper’s wider thesis, that events are a common primitive ontology for GRW, Bohm and ψ-antirealist views, shows compatibility only, and Dorato concedes the difference from Esfeld could be verbal. | Proposed |
| THEORY-657 | If an emergent property is one that the parts lack, then the other marks commonly given for emergence are separate questions about each system and not consequences of it: established condensed-matter cases show novelty without a discontinuity, a discontinuity without novelty, novelty that was predicted first, and novelty with a rigorous reduction | McKenzie (2025), LIT-141, read in full in NOTE-124. The book stipulates novelty as the definition and runs twelve further characteristics over about thirty cases. The Kondo effect is novel and continuous; the liquid–gas transition is discontinuous and adiabatically connected; BKT and the hexatic phase were predicted before they were found; Butterfield’s cases are novel and reduced. NOTE-124 says no THEORY follows from the book as a whole, since its definition is stipulated and the logical relations among the characteristics are left open by its own account (§24). This is the part of it that the counterexamples carry. | Proposed |
| THEORY-658 | Whether an account of organismal goal-directedness must separate genuine teleology from mere self-organisation, such as a candle flame, depends on what the account is for: a scientific model of agency need not and perhaps cannot draw the line, while an account of how mind and value fit into nature may have to, and need not be operationalisable | Nahas & Sachs (2023), LIT-192, read in NOTE-094 from the accepted manuscript. A metatheoretical argument: naturalising teleology serves at least two relatively autonomous projects, advancing biology and settling the naturalism debate, with different success criteria. It is worked on one dispute, the demarcation from dissipative structures. The positive pluralism (Deacon for naturalism, Walsh and the organisational approach for biology) is only “tempting to suggest”, and the boundary between the projects is never drawn. | Proposed |
| THEORY-659 | In the EEAS’s 2024 sample of 505 foreign information manipulation incidents, the overt state voice is a small core: of the 2,055 channels that recur across incidents, 20% are attributed to Russia, 3.5% to China and 76.5% are not attributed, after some 28,000 disposable inauthentic accounts are set aside; the sample is not representative, and the four-tier Exposure Matrix used to grade channels’ ties to a state is unvalidated | European External Action Service (2025), LIT-084, the 3rd EEAS report on FIMI threats, read in NOTE-060. A description of what the EEAS monitored, which the report itself says is not a basis for general trends. The 76.5% is a share of a filtered co-involvement graph, not of the 38,000 channels, though the report’s conclusions restate it as such. The Exposure Matrix grades attribution in four tiers by evidence and treats it as revisable; no inter-rater test or worked classification is given, and the strongest evidence is proprietary or classified. | Active |
| THEORY-660 | The local branching geometry of physical tree networks, neurons, blood vessels, trees, corals and plants, is set by minimising the surface area of tubes that must keep a minimum circumference, not by minimising length: this predicts trifurcations once links are thick relative to their separation (χ = w/r above about 0.83) and orthogonal sprouts once one branch is much thinner than the other two (ρ = w′/w below about 0.6), both departures from Steiner trees that the data show qualitatively | Meng, Piazza, Both, Barzel & Barabási (2026), LIT-069, read in full with the SI in NOTE-075. Only two symmetric motifs are solved, each by a local, penalised optimiser started from the Steiner layout; the “exact” mapping to string worldsheets holds for a problem the paper does not solve. The random-terminal prediction is a sigmoid fitted to one tetrahedron, trifurcations are partly made by a merging rule, the one robustness check moves the key statistic 4.3-fold, and the sprouting breakpoints are chosen per dataset with no null. Real motifs are about 25% longer than Steiner, which the model leaves unexplained. | Proposed |
| THEORY-661 v4 | In a nearly decomposable system, where interactions within subsystems are much stronger than interactions between them, each subsystem’s short-run behaviour is approximately independent of the others’, and in the long run each depends on the others only through their aggregate behaviour; so a hierarchy defined by intensity of interaction separates fast dynamics inside its parts from slow, aggregate dynamics between them | Simon (1962), LIT-905, read in full in NOTE-704. The two propositions are a theorem of Simon & Ando (1961), cited and not reproduced, and established since. Simon widens hierarchy to any nesting of interrelated subsystems, with or without authority, identified by who interacts with whom. His claims that social systems are prominently nearly decomposable, and that higher organisational levels run slower, are assertion and “probably true”. The watchmaker argument is a model whose numbers he says not to take seriously. | Active |
| THEORY-662 | The feeling of fluency is an inference about the precision of one’s own processing, triggered by a change in precision against expectation; because its cause is internal and not given to introspection, a felt discrepancy is attributed to the most salient external source, as familiarity, liking or a sense of error | Brouillet and Friston (2023), LIT-957, read in NOTE-785. A perspective essay with no model and no new data. It joins Whittlesea’s discrepancy-attribution hypothesis to precision-weighting. The part with moderate support is the reviewed finding that fluency judgements follow discrepancy from expected fluency (the hension effect and its extensions), reported secondhand. The precision reading and the felt/unfelt levels are proposals. “Felt” here means attended and reportable, not phenomenal, and fluency is not offered as affect. | Proposed |
| THEORY-663 | Altruism between non-relatives can be selected when each act costs the giver less than it benefits the recipient, the same partners meet often and symmetrically, and help is withheld from those who do not return it; in humans, moralistic aggression, gratitude, sympathy and guilt are adaptations that regulate such exchange, and selection then favours sham versions of each and the ability to detect them | Trivers (1971), LIT-510, read in full in NOTE-402. A verbal model, with a Prisoner’s Dilemma sketch Hamilton communicated, followed by a functional account of the human emotions that would regulate reciprocity. The model is plausible and was later formalized. The psychology is fitted to 1960s social-psychology findings, mostly on American students, and the heritability of the dispositions is assumed. Trivers knows “of no psychological studies on the detection of sham moralistic aggression and sham guilt” (p. 51). His “unfairness” is inequity in exchange, not the division of a disputed resource. | Proposed |
| THEORY-664 | In a finite-dimensional probabilistic theory with unrestricted effects and local tomography, if every system can steer each of its own states from a composite with a copy of itself, every irreducible state space is homogeneous and weakly self-dual; steering does not yet give strong self-duality, so it stops short of the Jordan-algebraic and quantum state spaces | Barnum, Gaebler & Wilce (2009), LIT-081, read in full in NOTE-082. A bipartite state steers its marginal iff its map on effects is a strong quotient of order intervals (Thm 5.4). With matching dimensions a steering state is an order-isomorphism, and a cone is homogeneous iff every interior state purifies to an isomorphism state (Thm 4.1). Hence universal self-steering gives homogeneity and weak self-duality (Prop. 5.8). The weaker Prop. 5.7 is thinly argued. The C*-algebraic conclusion of §6 needs strong self-duality, which the paper assumes rather than derives. | Active |
| THEORY-665 v2 | Asserting is undertaking a commitment that entitles others to reassert it and carries a responsibility to show entitlement if challenged; every interlocutor keeps score of everyone’s commitments and entitlements, so the score is doubly perspectival, and a speech act’s significance is the change it makes to the scores, fixed by its content’s inferential role | Brandom (1994), LIT-794, skimmed in NOTE-622: the Preface and the core of chapter 3 only. This states the deontic scorekeeping model of assertion, not the book’s arguments for it, and rests on a skim. By the author’s account the model is an idealization limited to semantic inference, with implicature left to an outer shell. It gives no single objective score, only scores kept from each perspective. | Proposed |
| THEORY-666 | A system that produces itself, a network of production that regenerates the components which produce it and constitute it as a distinguishable unity, has by that fact an intrinsic purpose, the maintenance of its identity, and with it a point of view, valence and a world as distinct from an environment, so that teleology in organisms is real and not an observer’s as-if; the account is stated for the cell, and a multicellular organism is not itself autopoietic | Weber & Varela (2002), LIT-1018, read in full in NOTE-720. An essay of exegesis and convergence: Kant’s natural purposes read non-reductively, Jonas’s metabolism-based philosophy of the organism, and autopoiesis. The step from self-production to purpose is asserted (“Bluntly stated”), the step to subjectivity is Jonas’s phenomenological inversion, and no observable is proposed for the “empirical feature” the conclusion claims. What sets autopoiesis apart from dissipative structures is placed in “concern”, not in organisation. One paragraph runs from self-maintenance to a right to life. | Proposed |
| THEORY-667 | Gender and race, defined as a feminist and antiracist theory needs them, are hierarchical social positions: a woman is someone subordinated in part because she is taken to have bodily features presumed to show a female’s reproductive role, a racialized group is one subordinated or privileged in part because its members are taken to have features presumed to show ancestry from a region, and on these definitions both are real, social and contingent | Haslanger (2000), LIT-480, read in NOTE-394. An explicitly ameliorative (“analytical”) account: the definitions are chosen for what a critical theory needs, and the author is “less committed to saying that this is what gender is and what race is” (p. 52). It is tied to a descriptive claim, that our gender and race talk tracks social kinds obscured by its manifest content (p. 34), which the paper asserts and does not test. Its empirical premises about race are uncited. Not a discovery about bodies, and not a claim that every female is a woman in its sense. | Proposed |
| THEORY-668 | When the encoder is restricted to prunings of one fixed hierarchy of nested partitions, any non-negatively weighted sum of relevant information, irrelevant information and compression decomposes into per-node terms, so a bottom-up recursion finds the unique optimal tree with fewest leaves exactly in linear time, while greedy top-down splitting can miss information lying below a level that carries none; penalising irrelevant information only prunes the information-bottleneck tree | Larsson, Maity & Tsiotras (2022), LIT-868, read in full in NOTE-676, every proof followed step by step. The decomposition is the chain rule for refinements, and the recursion is the classic bottom-up pruning of a fixed tree. NOTE-676 declined a THEORY as exact but narrow; it is filed because the reading supports it as stated and its greedy-failure point bears on how hierarchy is measured. The hierarchy is given, not found, and the evaluation is one image. | Active |
| THEORY-669 | Reading the universal quantum state as nomological escapes the costs of reading it as a field only by paying in the theory of laws: on the strong reading, modelled on the classical Hamiltonian, a time-dependent ψ makes laws time-indexed unless the universal state is time-independent, as Wheeler–DeWitt would make it; on the weak and functionalist readings ψ need be neither unique nor time-independent, but only within an extended Humeanism whose criterion would equally make classical fields nomological | Chen (2018), LIT-204 (NOTE-175), maps the realist readings and splits the nomological one into strong and weak. Belot (2011), LIT-100 (NOTE-110), ranks the costs of ψ-as-law: time-indexed laws are the serious obstacle, grades of necessity tolerable. Allori (2021), LIT-200 (NOTE-154), makes ψ an ingredient of the law, which may be time-dependent and non-unique, and so concedes Belot’s point that ψ behaves like an initial condition. Each move is an informal argument. Chen reports, without endorsing, the objection that the weak reading is too cheap, and Allori’s reply embraces the case it treats as a reductio. | Proposed |
| THEORY-670 | Ordinary dispositions can be modelled as restricted possibilities individuated by their manifestation alone: ‘fragile’ as manifestation in a sufficient proportion of cases over maximally varied external circumstances, ‘breakable’ as plain possibility; grading by closeness to an ideal world fails for any choice of ideal | Vetter (2014), LIT-109, read in full from the penultimate draft in NOTE-125. A proposal, which the paper says it does not show superior to the conditional conception (pp. 6, 26). Its strongest part is negative: for any ideal world, an Achilles’-heel block that breaks only there counts as fragile, so closeness grading fails. The positive proportion measure is not defined, and the finite, maximally varied set of cases it counts over is admitted to be non-unique. The evidence is ‘-able’ semantics and a COCA count in which none of 226 relevant uses of “disposed to” ascribes a standing tendency to an inanimate object. Finks and masks are left unsolved, and dispositions of fundamental science are set aside. | Proposed |
| THEORY-671 | An open system with enough internal degrees of freedom settles, among its possible steady states, into the one of maximum entropy production; this selects among steady states, where Prigogine’s minimum principle only describes relaxation toward one | Kleidon (2009), LIT-519, read in NOTE-423, states the principle and its Earth-system applications; Dewar (2003), LIT-521, read in NOTE-426, is the derivation it cites. The applications are model fits, mostly reported, many by the author. The derivation needs a mean-field step and an unargued assumption about path counts, and does not reach far from equilibrium (THEORY-676). “Sufficient degrees of freedom” is never made operational, so a failure can always be read as too few. The advocate’s own verdict: “no one would argue that MEP is well established”. | Proposed |
| THEORY-672 | In the iterated Prisoner’s Dilemma with a probability w of meeting again, no strategy does better against an established TIT FOR TAT than TIT FOR TAT does against itself if and only if w ≥ (T−R)/(T−P) and w ≥ (T−R)/(R−S); always defecting is stable for every w, a cluster of reciprocators can invade it, and a nice stable strategy resists clusters, but the stability is only neutral, since always cooperating ties | Axelrod & Hamilton (1981), LIT-498, read in full in NOTE-411. Against TIT FOR TAT the best reply is always-defect or alternation, which gives the condition on w. The cluster result and the “ratchet” are explicit payoff comparisons. “Evolutionarily stable” here means no mutant does better, which is weaker than Maynard Smith and Price’s definition: always cooperate does exactly as well. The model is deterministic and error-free. Tournament robustness is a separate, empirical claim about the strategies people submitted. | Active |
| THEORY-673 v2 | The Price equation follows from any ancestor–descendant mapping in a closed population and is, like f = ma, a generalization-sketch: a schema that is empty of predictions until a specific model supplies entities, characters, time step and causes, whose value lies in unifying and guiding model construction, so the charges that it is a tautology or lacks predictive power and dynamic sufficiency ask of it what only its specialisations can supply | Luque (2016), LIT-205, read in NOTE-101 from the PhilSci manuscript. The derivation and the diallelic re-derivation are strong; the generalization-sketch reading is a moderate argument by analogy with f = ma plus two case studies, whose authors recovered results already derivable otherwise. The reply to “tautology” answers the word, not the critics’ point, which Luque concedes in §7.2. The paper’s prescription, that biologists should adopt the equation, is asserted without comparison. | Proposed |
| THEORY-674 v2 | In Garg and Fetzer’s GPT-4o-mini extraction from NBER and CEPR working papers, edges kept in at least 4 of 9 passes and never checked against human labels, the mean per-paper share of edges labelled as backed by difference-in-differences, instrumental variables, an RCT, regression discontinuity or synthetic control rose from 7.7% in 1990 to 31.7% in 2020, at every overlap threshold; the paper’s per-decade slope fell from +0.0187 to +0.0011 once method mix and graph volume were controlled | Garg & Fetzer (2024; arXiv v2 2026), LIT-079, read in full in NOTE-083. GPT-4o-mini, nine passes per paper over the first 30 pages of 44,852 working papers, edges kept in at least 4 of 9 passes. The direction of the trend holds across overlap thresholds, its level does not (mean causal share 0.152 at EO = 1, 0.270 at EO = 9), and it nearly vanishes once method mix and graph volume are controlled. Validation covers paper-level method labels only, with RCT precision about 0.02. The association of causal structure with top-five publication rests on year-fixed-effect regressions over different subsamples and is not part of this claim. Promoted 2026-10-20 on the measurement alone (ADR-047 v3); the economics claim is held as THEORY-824. | Active |
| THEORY-675 | Without a shared stable start, the linear barrier between solutions of one objective depends on the structure of the training data: between GCNs it falls with graph density and feature separability and is highest at middling homophily, and between federated-averaging models it grows with client heterogeneity and falls with width | Li et al. (2025), LIT-676, read in NOTE-529: on synthetic CSBM graphs the barrier between GCNs from different seeds falls with density and feature separability and peaks at middling homophily; GCN, GraphSAGE and GAT barriers are similar, an MLP’s differ. Zhou, Zhang & Tsang (2023), LIT-666, read in NOTE-517: FedAvg global models from one random start under more heterogeneous clients are separated by a larger line barrier, joined by a one-bend chain, and the barrier falls with width. Both readings named this account and held it back. The GNN proofs are missing and its barriers are plots; the federated bound treats heterogeneity as isotropic noise, and its lemma and theorem conditions conflict as written. | Proposed |
| THEORY-676 | Dewar’s information-theoretic derivation of maximum entropy production does not reach the far-from-equilibrium regime where the principle is applied: the 2003 route needs a mean-field step and an unargued assumption about path counts, the 2005 route’s orthogonality condition, which yields both maximum and minimum dissipation, holds only with linear constitutive relations, and the 2003 self-organized-criticality corollary is an artefact of a quadratic expansion | Grinstein & Linsker (2007), LIT-525, read in NOTE-422, against Dewar (2003), LIT-521, read in NOTE-426. The self-organized-criticality point was checked against Dewar 2003 and is correct. The linearity point concerns Dewar 2005, which the record could not read; it is held on the Comment’s account of its equations and on an exactly solvable spin chain, re-derived. The Comment removes one derivation and one application. It does not say MEP is false, and it says the existence of far-from-equilibrium extremal principles “has not been settled”. | Active |
| THEORY-677 | Under uncertainty about which beings are sentient, an appeal to precaution does not by itself fix which error is worse to make: precaution on behalf of a possibly sentient being and precaution on behalf of human liberty point opposite ways, and judging which mistake costs more turns on the very science in doubt | Schwitzgebel & Sinnott-Armstrong (2026), LIT-166, read in NOTE-116 from the September 2025 draft. A conceptual argument with worked cases, which the reading rates strong: “By itself, an appeal to precaution does not specify the type of error most to be avoided” (p. 8). Birch’s framework puts the burden on whoever risks harming a sentience candidate; Mill’s harm principle, read as a precaution, puts it on whoever would restrict liberty. The record holds the point, not the reviewers’ reading of Birch’s books, which it has not read. | Active |
| THEORY-678 v2 | In Stable Diffusion, a subject named in a two-subject prompt is left out of the image when its token governs no region of the cross-attention map early in sampling, and raising that token’s smoothed peak attention during the first half of sampling, by gradient steps on the latent with no retraining, brings the subject back; that this also fixes attribute binding is argued, not measured by the paper | Chefer, Alaluf, Vinker, Wolf & Cohen-Or (2023), LIT-806, read in NOTE-639, with T2I-CompBench++ (LIT-798, NOTE-610) for the binding measurement the paper lacks. Evidence is on 276 templated two-subject prompts by CLIP image–text similarity, BLIP-caption similarity and a 65-person preference study (77–91% preferred it); no neglect rate is reported, before or after. NOTE-639 filed no THEORY, because the paper’s method is machine-learning practice; the account of why subjects go missing is a finding about the model and is filed here as Proposed. | Proposed |
| THEORY-679 | For dynamics obeying detailed balance in a heat bath, the heat released in a transition between observer-defined macrostates is bounded below by the log-odds against its reversal less the internal entropy change; where a replicator’s likeliest way back is a copy decaying within one generation, the bound grows with the copy’s durability and the speed of copying, not with the information copied | England (2012; J. Chem. Phys. 2013), LIT-515, read in NOTE-419. The general bound, β⟨ΔQ⟩ + ln π(II→I) + ΔS_int ≥ 0, is a coarse-grained second law and was re-derived. Applied to replication it gives a heat cost of about 2n ln(n τ_decay/τ_div) per copy, which falls away as division slows. The numbers for E. coli (within a factor of three of the bound) and RNA rest on an upper bound on the reverse probability that is argued from biology, not proved, and on an internal-entropy term set “arbitrarily”. It prices finite-time irreversibility, not information, and draws no line between living and non-living replicators. | Active |
| THEORY-680 | Emotion regulation is a set of processes distinct from emotion generation, by which people influence which emotions they have, when, and how they are experienced and expressed; regulatory acts can be sorted by the point in the generative sequence where they act, and acting before response tendencies form (reappraisal) has different consequences from acting after (suppression) | Gross (1998), LIT-554, read in NOTE-429, the founding review. It reports no data. The five families (situation selection, situation modification, attentional deployment, cognitive change, response modulation) are “working distinctions”. The antecedent and response contrast rests on a handful of film studies it cites: reappraisal lowered negative experience, suppression did not reliably do so and raised sympathetic activation. The paper’s own first open problem is whether regulation can be told apart from generation at all. | Proposed |
| THEORY-681 | If every real idea derives from an impression, there is no idea of a simple self persisting through life; the mind is a bundle of perceptions, and the identity ascribed to it is produced by the imagination passing easily along resemblance and causation, as with a rebuilt ship or a growing oak, though Hume’s Appendix concedes that this does not explain what unites the perceptions | Hume (1739, with the Appendix of 1740), LIT-451, read in NOTE-386. The negative half is as strong as the copy principle. The mechanism of the fiction is argued by analogy from cases of usage. The account of what unites the bundle is withdrawn by its author, who names the two principles he cannot reconcile. It does not say there is no self in any sense, and it leaves identity “as it regards our passions” to Book 2. | Proposed |
| THEORY-682 | The time-average of a single threshold (Hill) response to a periodic signal is independent of the signal’s period for a fixed waveform, so a frequency cannot be read by one sigmoidal stage; two cascaded stages can read it, because the first changes the waveform with period; and a delayed kinesin–dynein signalling loop whose period grows with axon length, read out this way and coupled to protrusion and contraction, can hold an axon at a stable length | Folz, Wettmann, Morigi & Kruse (2018; PRE 2019), LIT-034, read in full in NOTE-067. The period independence is proved, for signals that differ by a time rescaling only; the two-stage readout is shown numerically and in the Heaviside limit; the loop’s minimum length and ω ≈ √3 v/L for long axons come from linear stability analysis. The length control is a lumped delay-differential model with one parameter set and the motor velocity v never stated, so its absolute lengths, about 125 µm, cannot be reproduced. A proof of mechanism, not a model fitted to axons. | Proposed |
| THEORY-683 | Permuting a fixed set of few-shot examples moves a GPT-family model’s classification accuracy between near chance and near the supervised state of the art, at every model size tested; the good orders are specific to the model, the spread survives more examples and calibration, and bad orders mostly fail by predicting one label | Lu et al. (2021, ACL 2022), LIT-833, read in NOTE-626. All 24 orders of four balanced SST-2 examples give accuracies from about 50% to above 85%, in GPT-2 and GPT-3 models of eight sizes; Spearman correlations of order accuracy between sizes lie between −0.35 and 0.27 (175B against 2.7B: 0.05). The variance stays high up to 32 examples and after calibration. It is a measurement on causal GPT models and text classification, with the transfer analysis resting on one example set, and the paper finds no property of an order that predicts its effect. | Active |
| THEORY-684 | Experiencing oneself as a self that was there in the further past, seeking pattern in one’s life, fitting it to a story and falsifying it in the telling are separable, and fitting it to a story suffices for narrativity; on testimony that some normal people are Episodic and live good lives, neither the claim that people experience their lives as narratives nor the claim that a good life or full personhood needs it holds in general | Strawson (2004), LIT-452, read in NOTE-383. The separation of Diachronicity, form-finding, story-telling and revision is strong as conceptual analysis. That many normal people are Episodic rests on testimony, the author’s and that of writers he classifies, with no measure. It does not say that the remoter past did not happen to the human being, only to the self one now experiences oneself to be, and that metaphysical claim is asserted from earlier papers. | Proposed |
| THEORY-685 | The Mizohata–Takeuchi conjecture fails for every compact C² hypersurface with a point of non-zero curvature: for each large R a function and a weight violate it by a factor of order log R, which refutes Stein’s conjecture as stated and closes the Mizohata–Takeuchi route to loss-free endpoint multilinear restriction | Cairo (2025), LIT-030, read in full in NOTE-051, which checked the counting and exponent bookkeeping. The paper states the theorem for any C² hypersurface not lying in a hyperplane; the proof needs a curved point, which a connected such surface has. The incidence lemma (§4) is the step a non-specialist could not verify. The loss is log R, not a power, and the counterexample is a family indexed by R. It does not refute endpoint multilinear restriction itself. Its proposed local replacement has since been refuted with power loss on a dense family of surfaces, per the abstract of a later paper. | Active |
| THEORY-686 v2 | An observation modelled as a monotone map between preorders can show of a joined system more than the join of its observations of the parts, and out of a preorder with all joins the observations that preserve all joins, the empty join and infinite joins included, are exactly the left adjoints | Fong & Spivak (2018), LIT-803, Chapter 1, read closely in a Skimmed NOTE (NOTE-601) whose other chapters were seen only at their openings. Def. 1.93, after Adam, defines a generative effect as Φ(a) ∨ Φ(b) < Φ(a ∨ b). Prop. 1.111 and Thm 1.115 give that left adjoints preserve all joins and, from a source with all joins, only they do. The results are standard order theory, re-derived by the record because NOTE-601 is a skim. The absence of generative effects is weaker than preserving all joins, and does not characterise the left adjoints. | Active |
| THEORY-687 | For empirically equivalent dual theories read naively, adding the common core as a candidate world does not break the underdetermination, and neither do super-empirical virtues or an overarching theory: each route to a single actual world needs a further metaphysical principle, such as the identity of indiscernibles | Le Bihan & Read (2018), LIT-113, read in NOTE-152 from the accepted manuscript. A nontechnical survey whose central argument is informal. It assumes a duality relates empirically equivalent models (weaker than De Haro & Butterfield’s isomorphism of a bare theory), that each model is read naively and internally, and that structuralism is set aside. Its reading said it supports no existing THEORY directly; this files the conditional verdict the survey argues for, and nothing more. | Proposed |
| THEORY-688 | In an actor-critic learner that can choose temporally extended options as well as primitive actions, options that fit the task speed learning, while options with ill-placed subgoals slow it, and options that fit an earlier layout keep the agent from finding a newly opened shortcut, so hierarchy helps only with the right subroutines | Botvinick, Niv and Barto (2009), LIT-581, read in NOTE-451. Toy simulations in a rooms domain with pre-trained options. Doorway options sped learning; window options slowed it; with a shortcut opened, primitive-only agents found the shortest path on 75% of runs while doorway-option agents never used it (mean 11.79 against 9.73 steps). It is a result about the model. That people or brains work this way is the separate, proposed account THEORY-484. | Active |
| THEORY-689 | A mobile robot built from parallel layers of simple finite-state machines, each linking sensing to action by itself and combined only by one layer suppressing or inhibiting another’s signals, avoids obstacles, wanders and heads for distant places with no central world model, goal list or controller; shown at insect scale, on three layers of one physical robot | Brooks (1991, written 1987), LIT-436, read in NOTE-351. An existence proof by construction: the absence of central representation and control is true of the architecture by design, and the robot ran “for well over a year”. The evidence is described, not measured; three layers ran on a robot and six in simulation. The claims that coherence exists only “in the eye of an observer”, that representation is the wrong unit for most of intelligence, and that the method scales are assertion or labelled hypothesis. | Active |
| THEORY-690 | In the physical dualities examined, theoretically inequivalent duals turn out empirically inequivalent, so dualities yield no genuine in-principle underdetermination; where duals would contradict each other a cautious realist is warranted in committing only to their common core, and because the exact cases’ common cores are rich rather than empty, dualities give no support to structural realism | De Haro & Butterfield (2025), LIT-199, read in NOTE-178. A case-by-case argument over the book’s examples, with a logico-semantic fallback (each dual entails the common core) for a hypothetical genuine case. The rich-core verdict is argued from exact cases (bosonization, electric–magnetic duality, T-duality) and does not reach AdS/CFT or M-theory, where structural-realist readings were proposed and the common core is “partial … ongoing work in physics!”. The commitment holds only where an interpreted common core exists, which the authors say is not true in general. | Proposed |
| THEORY-691 | A self is an abstractum like a centre of gravity, posited by interpreting a person’s behaviour and talk, the brain’s own autobiography included; it is as determinate as that story, it can be authored by a process with no self in it, and a body holds as many selves as the points the best story coheres around | Dennett (1992), LIT-442, read in NOTE-364 from a copy-edited transcription. Argued by analogy and by thought experiments whose premises are stipulated, notably that a mindless machine could write a passable novel. It does not say the self is an illusion: a centre of gravity is a legitimate posit that figures in explanations. It is a claim about selves, not about consciousness or about what makes a person persist. | Proposed |
| THEORY-692 | Near equilibrium, steady states minimise entropy production and every fluctuation decays; far from it, the excess entropy production has no fixed sign, so a fluctuation can grow past an instability of the thermodynamic branch into a structure held up only by flows across the boundary, and thermodynamics supplies only a sufficient condition for such a state’s stability, not a principle selecting which structure appears | Prigogine (1977), LIT-516, read in full in NOTE-424, with Cross & Hohenberg (1993), LIT-527, skimmed in NOTE-418. Minimum entropy production holds only for steady states in the strictly linear regime with constant coefficients. Beyond it, non-negative excess entropy production suffices for stability; its failure is not shown to give instability. Which structure appears is left to kinetics, boundaries and fluctuations. Cross and Hohenberg find no global minimisation principle beyond a perturbative one near threshold, and quote Glansdorff and Prigogine conceding that “the search for a universal kinetic potential has proved to be unsuccessful”. | Active |
| THEORY-693 | In conversation, evaluating an object, positioning oneself and aligning with another speaker are three aspects of one stance act rather than three kinds of stance, because a stance takes a shared object and answers a prior stance, which are usually supplied by earlier turns; a resonant follow must mark its relation to the lead, with too or either in English | Du Bois (2007), LIT-779, read in full in NOTE-590. Argued from short excerpts of American English conversation (Santa Barbara and Longman corpora), with no counts. The co-occurrence of the three aspects is shown in chosen examples, not tested for separability; the too/either result rests on a separate study (Du Bois 2004) whose figures are not given. It does not treat a speaker who animates someone else’s stance, which it sets aside for Goffman. | Proposed |
| THEORY-694 | After every function associated with consciousness is explained (discrimination, integration, report, access, attention, control), why these functions are accompanied by experience remains open, because those phenomena are defined by their functions and experience, what it is like for the subject, is not; so experience cannot be reductively explained by any mechanism, though it may be related to the physical by further laws | Chalmers (1995), LIT-406, read in full in NOTE-336, with Nagel (1974), LIT-096, read in NOTE-089, for the subjective character it starts from. The test is whether “you have explained the function but not the phenomenon” is a conceptual mistake: it is for life and reportability, not for experience. The decisive premise, that any physical process could conceptually occur without experience, is asserted and deferred to a book the record holds unread. Nagel’s conclusion is weaker than Chalmers’s: physicalism not refuted but not yet understandable. Naturalistic dualism and the double-aspect theory of information are the proposals built on the gap, not part of it. | Proposed |
| THEORY-695 | Two quantum states can be broadcast if and only if they commute, and cloned if and only if they are identical or orthogonal; the theorem is proved for invertible density operators and marks a line within quantum theory, not a witness of nonclassicality | Fuchs (1995), LIT-018, §4.3, read in full in NOTE-021, from the Barnum–Caves–Fuchs–Jozsa–Schumacher manuscript. Fidelity cannot decrease under partial trace or under the broadcasting map, so broadcasting forces equality conditions that make ρ0 commute with the optimal-fidelity operator. Proved for invertible ρ0, ρ1 only. Spekkens’ epistricted classical theories (LIT-007) reproduce no-broadcasting, so the theorem states where broadcastability ends inside quantum theory and does not by itself certify nonclassicality. | Active |
| THEORY-696 | Under multiplicative noise, members that pool their resources and split them equally every step each grow faster in the long run than they would alone, with no complementarity, relatedness or reciprocity: N independent geometric Brownian motions that share keep their drift μ and cut their volatility to σ/√N, raising each one’s time-average growth rate from μ − σ²/2 to μ − σ²/(2N); the gain vanishes as their noise becomes perfectly correlated, and a sufficiently superior member does better alone | Peters & Adamou (2022), LIT-035, read in NOTE-059. The mathematics is correct and self-contained, and the paper’s own citations show the pooled-variance result was known (McCloskey, Winterhalder, Uitdehaag, Kennedy et al.). Sharing leaves the ensemble rate μ unchanged, so an analysis built on expectations sees no reason to share, and the time average does. It holds with zero cost, perfect pooling, unbreakable pacts and unconstrained growth. It is a sufficient mechanism in that model, not a solution of the cooperation puzzle, and not a showing that cooperation is the default. | Active |
| THEORY-697 | Sparse distributed memory’s read weights each stored pattern by the number of hard locations within the read radius of both query and pattern, a ball-intersection count that falls roughly exponentially in Hamming distance over a local window, so softmax attention over cosine similarity of unit-norm queries and keys, with a fitted inverse temperature, approximates the SDM read there; the approximation cannot hold globally, since the binary count vanishes beyond twice the radius, and its inverse temperature comes from a regression, not from the paper’s analytic bound | Bricken & Pehlevan (2021), LIT-269, read in full in NOTE-242, which re-evaluated the intersection formula and the fit. The exact intersection (Eq. 2) is checked against Kanerva’s lune formula and simulation; eight SDM and fitted-softmax variants retrieve almost identically on random patterns, MNIST and CIFAR-10, with three named exceptions. The intersection is a staircase in distance, the fit holds to about dv = 20 for d = 15, the analytic β of App. B.2 is about 2–2.5 times too small, and every optimal radius assumes random patterns and addresses. The GPT-2 “confirmation” and the cerebellar implementation of attention are argument, not demonstration. | Active |
| THEORY-698 | Thresholding linear attribute probes on a language model’s embeddings yields a complete concept lattice for any incidence whatever, so the lattice is guaranteed by construction; what the Lattice Representation Hypothesis measured is per-attribute agreement with GPT-4o annotations at F1 70–83, and no lattice law | Xiong (2026), LIT-267, read in NOTE-240. Theorem 1 is the basic theorem of formal concept analysis applied to the crisp relation got by thresholding Fisher-LDA probes, and it holds for every binary relation; the paper’s own proof plan says so. The empirical content is that the thresholded probes on three 7–8B models agree with a GPT-4o-annotated incidence at macro F1 69.7–83.2 and predict WordNet subsumption at F1 57.1–77.1. No closure, absorption or recovered-lattice comparison is tested, and the paper’s join is not a lattice join as written. It is not evidence that language models encode a lattice beyond the incidence. | Active |
| THEORY-699 | Adaptive self-maintenance across varied conditions is sufficient, without sentience, for having a good of one’s own, so insentient plants and a self-maintaining machine are welfare subjects while thermostats are not; but the line against thermostats is argued as one of degree, and the reasons such welfare gives are extremely weak | Bruckner (2025), LIT-120, read in NOTE-093. Proposed by abduction from agreed cases, not deduced (§4): an entity that “sustains, maintains, and renews itself in a way that responds and adapts to its environmental conditions” is a welfare subject. Plants and the hypothetical car Tessler qualify; governors, thermostats and missiles do not. The “autopoiesis” is a loose behavioural notion, not Maturana and Varela’s self-production, and the thermostat line is supported only comparatively. The answer to absurd obligations borrows Bradford 2023 and makes phenomenal consciousness decide how much such welfare matters. | Proposed |
| THEORY-700 | For jointly Gaussian stationary processes, Granger causality in Geweke’s generalized-variance form is exactly twice the transfer entropy, conditional and multivariate, at the regressions’ lags, because least-squares residual covariance is the partial covariance and a Gaussian’s conditional entropy is half its log-determinant plus a constant | Barnett, Barrett & Seth (2009), LIT-1171, read in full in NOTE-934. F_{Y→X|Z} = 2T_{Y→X|Z}, exactly, for population quantities. The proof is two identities and was checked. Sample agreement depends on the entropy estimator. Both quantities are predictive; the authors keep them apart from physical causation. | Active |
| THEORY-701 | Transfer entropy from J to I is the Kullback entropy of assuming that I’s next state, given its last k states, does not depend on J’s last l states, so it is zero exactly when J’s past leaves I’s transition law unchanged; unlike time-delayed mutual information it is directional and zero for static correlation, and it removes a common input only when that input is conditioned on | Schreiber (2000), LIT-1177, read in full in NOTE-940. The definition and its zero condition are exact. The comparison with delayed mutual information rests on two coupled-map lattices built with a known direction. The continuum-limit claim is asserted. The Letter’s tent-map coefficient appears to be twice what Eq. 4 gives. | Active |
| THEORY-702 | Transfer entropy is the average of a local transfer entropy, the log ratio at each observation of the destination’s next-state probability with and without the source given the destination’s past, which can be negative where the source misleads; the destination history must be long for it to exclude self-influence routed through the source; and conditioning also on the destination’s other causal parents (complete) can differ sharply from conditioning on its past alone (apparent), as in elementary cellular automata, where long-history local transfer entropy picks out gliders and domain walls | Lizier, Prokopenko & Zomaya (2008), LIT-1175, read in full in NOTE-943. The local decomposition is an identity; the claims about k and about particles rest on elementary CAs judged by eye. Three worked local values and rule 18’s XOR structure were checked. | Active |
| THEORY-703 | Weak emergence of a macro variable from micro variables can be measured as its Granger autonomy from them times their mean Granger causation of it, which is zero if it is independent of them or fully predicted by them; in a boids model this measure, and Granger causation from the flock’s centre of mass to each boid, are higher for flocking than for random or rigid motion; the measure is relative to the regression model and the variables included | Seth (2010), LIT-1170, read in full in NOTE-935. The definitions are exact; the evidence is two hand-built agent-based models. Seth concedes that the measure is epistemic: positive with missing micro factors or a limited predictor, zero with the system as predictor. Proposed until it is tested against an independent criterion. | Proposed |
| THEORY-704 | In a stationary multivariate time series whose components include every relevant process, with interventions that are isolated exogenous changes and no instantaneous causation, a missing Granger-causal edge from a to b means intervening on a has no effect on b at the next step, non-ancestry means no effect at any horizon, and a set whose observed past blocks every back-door path into b’s ancestors identifies the effect from observational data, as a multi-step linear-predictor coefficient in the Gaussian case | Eichler & Didelez (2007), LIT-1164, read in full in NOTE-941. The back-door results are proved; the edge-to-effect statements in the conclusion are said to follow by the same reasoning; the front-door proof is deferred. All conditions are sufficient, and Assumption 2.3 is untestable from observational data. Two worked effects were checked. | Active |
| THEORY-705 v2 | For a target and two sources with finite alphabets, if unique information is to depend only on the two source–target pair marginals, then the minimum of the conditional mutual information over all joints with those marginals is an upper bound on every non-negative decomposition’s unique information, and the shared and synergistic information it implies are lower bounds; this unique information vanishes exactly when the other source is Blackwell-sufficient, and the measures are non-negative, satisfy the bivariate partial-information axioms and the identity property, and do not extend to three sources on the partial-information lattice | Bertschinger et al. (2014), LIT-1162, read in full in NOTE-937. The bounds, the Blackwell characterisation and the properties are proved. The motivating property is argued, not derived. Example 30 and the Table 1 rows reproduce, except two entries that conflict with the paper’s own Proposition 18. Under this measure, the record’s transfer-entropy examples split exactly as under I_min. | Active |
| THEORY-706 | Any redundancy function defined on the lattice of antichains of sources, ordered so that a collection precedes another when every source of the latter contains one of the former, has a Möbius inverse that decomposes the information a set of sources gives about a target into partial-information atoms summing to every subset’s mutual information; for the I_min redundancy, the expected minimum specific information over sources, every atom is nonnegative, and interaction information is a signed mixture of atoms, synergy minus redundancy for three variables | Williams & Beer (2010), LIT-1172, read in full in NOTE-936. The lattice, the inversion and the nonnegativity proofs are exact and were followed; the lattice sizes and the 3-parity and three-copies cases were checked. What is not shown is that I_min measures shared information: it gives two independent copied bits 1 bit of redundancy (Harder, Salge and Polani). | Active |
| THEORY-707 | Transfer entropy is not a measure of information flow, if flow means information in the target attributable solely to the source’s past: as a conditional mutual information it equals the source’s unique information plus its synergy with the target’s past, so it can credit a full bit to a source that carries none alone (Y_t = X_{t−1} ⊕ Y_{t−1}) and report zero from each of two sources that jointly fix the target (Z_t = X_{t−1} ⊕ Y_{t−1}); conditioning on further series, as causation entropy does, has the same fault | James, Barnett & Crutchfield (2016), LIT-1165, read in full in NOTE-945. Both examples are exact and were recomputed. The decomposition holds for any PID satisfying the consistency equations. The conclusion is relative to the authors’ definition of flow; transfer entropy as predictive improvement is untouched. The claims about directed information, interventional flow and Gaussian systems are cited or conjectured. | Active |
| THEORY-708 v2 | The I_min redundancy credits two independent sources with shared information whenever each reduces surprise about the same target outcomes, so it gives two independent bits copied into the target 1 bit of redundancy; a bivariate redundancy built from reverse information projections, each source’s information less what is lost when its posteriors are replaced by mixtures of the other’s, satisfies symmetry, self-redundancy, monotonicity and the identity property, gives a nonnegative decomposition, and agrees with I_min on XOR, AND and their compositions but can reverse the state-independent/state-dependent split of a transfer entropy | Harder, Salge & Polani (2013), LIT-1168, read in full in NOTE-944. The counterexample, the axioms and the nonnegativity proof are exact; every Table I value and both transfer-entropy examples were recomputed. The identity axiom and “mechanistic redundancy” are positions, not results, and the measure is bivariate only. | Active |
| THEORY-709 | Mutual information between continuous variables can be estimated from k-nearest-neighbour statistics, with the joint k-th-neighbour distance in the maximum norm fixing the scale at which marginal neighbours are counted, so that the biases of the three entropy estimates largely cancel; the one approximation is a locally constant density, the systematic error scales with k/N, and exactness for independent variables is observed in every tested case but not proved | Kraskov, Stögbauer & Grassberger (2004), LIT-1163, read in NOTE-938 (formal sections in full, numerics at lower resolution). The estimators are derived up to one approximation and one neglected correction; the rest is numerical. Checked by simulation on correlated Gaussians. | Active |
| THEORY-710 | In a finite causal Bayesian network, a set of nodes is causally independent of another, imposing a third, for every choice of mechanisms exactly when every directed path between them passes through the third; information flow, conditional mutual information computed from interventional instead of observational distributions, vanishes under causal independence, and it can differ from transfer entropy and conditional mutual information in either direction | Ay & Polani (2008), LIT-1174, read in full in NOTE-946 from the 2006 preprint. Theorem 2 and Prop. 3 are proved; Examples 3–6 were recomputed. Example 6’s one bit holds at k = 1 and fails for k ≥ 2 as stated. The measure needs the mechanisms, and estimation and identification are not addressed. | Active |
| THEORY-711 | Directed information from an input sequence to an output sequence, the sum over time of the information the inputs up to now carry about the current output given the past outputs, is at most their mutual information and equal to it when the channel is used without feedback; in a causal system it bounds what the output reveals about the source, so feedback cannot raise a memoryless channel’s capacity; and the usual definition of a memoryless channel holds only without feedback | Massey (1990), LIT-1166, read in full in NOTE-939 from the author’s preprint. Three short theorems, all checked; the feedback inequality also checked numerically. “Causal” is Massey’s factorization condition, not intervention. That directed information is full-history transfer entropy plus instantaneous terms is the record’s derivation. | Active |
| THEORY-712 v2 | Under any partial information decomposition satisfying the consistency equations, a transfer entropy T_{Y→X} = I(X_{t+1}; Y_t | X_t) is the unique information of the source’s past about the target’s next state plus the synergy of source and target pasts, which Williams and Beer call state-independent and state-dependent transfer; time-delayed mutual information is the unique part plus redundancy; with the I_min redundancy the state-independent part alone suffices for perfect open-loop control, and a two-source transfer entropy splits into unique, redundant and synergistic transfer | Williams & Beer (2011), LIT-1176, an arXiv preprint, read in full in NOTE-942. The two-term split is an identity from the consistency equations; the sizes of the terms, the control theorem and the multivariate split use I_min, which the record has not read argued for. The one-parameter family and the three corners of the two-source family were recomputed. The text mislabels the synergistic corner. | Active |
| THEORY-713 | No redundancy measure on the Williams–Beer partial-information lattice can satisfy symmetry, self-redundancy, monotonicity, the identity axiom and non-negative atoms once there are three sources: for two independent bits, their XOR and a target that copies all three, identity forces three one-bit atoms under a two-bit total, so one atom is at most −1 bit, and a multivariate decomposition that keeps identity must give up non-negativity or the lattice | Rauh, Bertschinger, Olbrich & Jost (2014), LIT-1202, read in full in NOTE-965. A proved impossibility, checked by hand and by script. It also uses invariance of redundancy under relabelling the target, which is not stated as an axiom. I_min escapes it by failing identity, Ince’s I_ccs by accepting the −1-bit atom. | Active |
| THEORY-714 v3 | Ince’s I_ccs, the expected local co-information over only those events where every source, the joint source and the overlap change the target’s surprisal in the same direction, under the maximum-entropy joint that preserves the source–target and joint-source marginals, is symmetric and self-redundant and satisfies the independent identity property; it fails Harder et al.’s identity and monotonicity, so its atoms can be negative, and, though its paper says otherwise, it fails subset equality | Ince (2017), LIT-1201, read in NOTE-968. The definition is exact, and three of the four properties the paper claims hold; subset equality does not (re-derived 2026-10-20), and every discrete example reproduces. That the dropped properties ought to be dropped, and that unique information depends on the source–source marginal, are argued, not proved. Whether it is the right redundancy measure is open (QUESTION-223). It meets Rauh et al.’s −1-bit bound exactly on XORCOPY. | Active |
| THEORY-715 | The information about a target carried by the Gács–Körner common random variable of the sources is a redundancy defined for any number of sources that is nonnegative, target-monotone and no larger than I_min, and is a lower bound on any reasonable redundancy; but it counts only deterministic shared structure, so it is zero whenever the sources’ joint distribution has full support, fails the identity property and continuity, and gives negative synergy already for two sources | Griffith, Chong, James, Ellison & Crutchfield (2014), LIT-1203, read in full in NOTE-967. The lemmas are short and exact, and every example was recomputed, with Harder, Salge and Polani’s copy family and a three-source copy added. It is the record’s one redundancy defined for n > 2, and it does not have the identity property there or for n = 2. | Active |
| THEORY-716 | Synergy can be measured as the whole minus the union of its parts, the union information being the least information the sources could jointly carry about the target with every source–target marginal held fixed; this synergy lies between WholeMinusSum and Williams and Beer’s S_max, which respectively subtract redundancy and count unique information as synergy, and for two sources it is Bertschinger et al.’s synergy, so independent sources can share information about a target, as the authors’ last version concedes against their first | Griffith & Koch (2014), LIT-1204, read in full in NOTE-966, v6 with v1–v2 checked. The definitions, the criticisms of S_max, WMS and ΔI, and the properties proved in Appendix C are exact, and every Table 1 value for two predictors was recomputed. The identification with Bertschinger et al.’s CI for two sources is the record’s derivation. Monotonicity is claimed without proof, and the S_max bound’s proof has a step the reading could not reconstruct. | Active |
| THEORY-717 | For experiments with finitely many states and finitely many outcomes, being at least as informative in every decision problem is the same as being reproducible from the other by a Markov matrix | Blackwell (1953), LIT-781, Theorems 4–6, read in NOTE-595: the Sherman– Stein theorem, with a new minimax proof. With n states and finite outcome sets, write experiments as n × N Markov matrices P and Q. Every risk vector Q attains in every decision problem is attainable with P exactly when Q = PM for some Markov matrix M. The arbitrary-outcome extension is THEORY-156, still Proposed. A qualitative order: most pairs are incomparable, and it says nothing about how far apart they are. | Active |
| THEORY-718 | In a linear-in-parameters model with Gaussian noise and a Gaussian prior, the evidence is exactly the best-fit likelihood times an Occam factor set by the posterior curvature, and when the design grows linearly with n that factor costs (k/2) log n | MacKay (1992), LIT-623, Eqs. 5–6 with Eqs. 16 and 19–20, read in NOTE-471: for y = Φw + noise with Gaussian noise of precision β and the prior w ~ N(0, α⁻¹I) on k weights, the posterior is exactly Gaussian, so the evidence is exactly P(D|w_MP) times the Occam factor P(w_MP)(2π)^{k/2} det^{-1/2}A, with A = αI + βΦᵀΦ. If ΦᵀΦ/n converges to a positive-definite matrix and w_MP stays bounded, the log Occam factor is −(k/2) log n + O(1). Exact for this model class only. The general regular case and the singular case are THEORY-087, which is Proposed. | Active |
| THEORY-719 | On a finite augmentation space, over unconstrained functions of the two views, the spectral contrastive and NT-Logistic losses are both minimized at the positive-pair density ratio | Johnson, El Hanchi & Maddison (2023), LIT-258, App. B.2–B.3, read in NOTE-751: on a finite augmentation space, with every function of the two views allowed, the spectral contrastive loss is minimized by K⁺ = p⁺/(p⊗p) exactly, and the NT-Logistic loss with equal positive and negative classes by the log-odds log K⁺, so its exponentiated score is K⁺. Population optima over unconstrained functions only; not what an encoder reaches, and not InfoNCE, which is THEORY-001’s open part. | Active |
| THEORY-720 | Classical simulations between no-signalling empirical models on finite scenarios, which may change the cover, never create contextuality: a model is non-contextual exactly when the empty model simulates it, the non-contextual fraction cannot fall along a simulation, strong contextuality is reflected backwards, and only non-contextual models can be cloned | Karvonen (2018), LIT-846, Theorems 4.1, 4.3 and 4.5, read in NOTE-651; Abramsky, Barbosa, Karvonen & Mansfield (2019), LIT-847, Theorems 21 and 22, read in NOTE-647. A classical simulation answers each measurement of the target by a jointly measurable set of the source’s, with shared classical randomness, so the cover may change. Non-contextual models are exactly those the empty model simulates, NCF cannot fall along a simulation, strong contextuality is reflected backwards, and a model clones itself only if it is non-contextual. No-signalling models on finite scenarios only. Which maps are simulations is THEORY-174’s open half. | Active |
| THEORY-721 | On a complex Hilbert space no orthonormal basis or tensor factorisation of given dimensions is distinguished by the space alone, and orthonormal bases correspond exactly to commutative special †-Frobenius algebras; over the reals that correspondence fails | Three results THEORY-017 rested on, held apart from its synthesis. (a) The unitary group acts transitively on the orthonormal bases of a finite-dimensional Hilbert space, and on its tensor factorisations of given dimensions, so neither is fixed by the space; a non-degenerate self-adjoint operator fixes a basis up to phases, and its invariant content is its spectrum. (b) Over ℂ, commutative special †-Frobenius algebras correspond exactly to orthonormal bases: Coecke, Pavlovic & Vicary, LIT-274, Thm 5.1 and §6, in finite dimension; Abramsky & Heunen, LIT-275, Thm 22, for the non-unital ones satisfying the H*-axiom, in any dimension. (c) Over ℝ it fails: ℂ as a real algebra, with multiplication scaled by 1/√2, is a commutative special †-Frobenius algebra with no nonzero copyable vector. | Active |
| THEORY-722 | In Contextuality-by-Default 2.0, whether a system of non-binary variables is contextual depends on which variables represent the measurements: coarse-graining can turn a noncontextual system into a contextual one, while for connections of two variables, and for consistently connected systems, CbD 1.0 and 2.0 agree | Dzhafarov & Kujala (2017), LIT-831, Examples 1–3 and Section 4, read in NOTE-643 (claims C4 and C6). Under multimaximal couplings, lumping values of non-binary variables can destroy every multimaximal coupling, so a noncontextual system becomes contextual. The verdict on a fixed set of measurements therefore depends on which variables represent them. For connections of two variables, hence cyclic systems, and for consistently connected systems, the 1.0 and 2.0 definitions agree. It does not say the coupling choice changes verdicts in larger connections, which is THEORY-168’s asserted part. | Active |
| THEORY-723 | For the final embedding and unembedding of a softmax model, the output distribution fixes the representations only up to an invertible linear map, and whether closeness in distribution bounds representational dissimilarity depends on the distance: not for KL in the saturation regime, but yes for the log-likelihood variance distance | Nielsen et al. (2025), LIT-253, read in full in NOTE-738, with Harvey, Larsen & Williams (2023), LIT-250, for the kernel side. What is observed fixes a representation only up to that observation’s symmetry group: a centred linear kernel up to a translation and an orthogonal map (THEORY-004), and a softmax output distribution up to an invertible linear map of the embedding with the inverse transpose on the unembedding (Thm 2.2). KL can go to zero while the embeddings stay non-linearly related (Thm 3.1, Cor. 3.2), but d_LLV ≤ ε gives d_f,g ≤ 2Mε (Thm 4.7). Final layer only. It does not say what the Platonic hypothesis means; that is THEORY-002. | Active |
| THEORY-724 | For a linear system du/dt = A(t)u, non-normality is necessary for time dependence to destabilize an operator that is uniformly stable at every instant, and a non-normal operator neutral at every instant can be asymptotically unstable under switching | Farrell & Ioannou (1996), Part II, LIT-929, eq. 12 and §4, read in NOTE-842. Because d‖u‖²/dt = u†(A + A†)u, the first Lyapunov exponent lies between the long-run averages of the extreme eigenvalues of the Hermitian part. For a normal operator the largest is the spectral abscissa, so an operator that is normal and uniformly stable at every instant has a negative exponent. A switched undamped oscillator, neutral at every instant, has a positive exponent. The stochastic genericity results are THEORY-325’s, still Proposed. | Active |
| THEORY-725 | On the court agenda {P, Q, R, R iff (P and Q)} under universal domain, proposition-wise majority voting is not robustly rational, while the premise-based procedure is, and it makes the group’s judgments a function of the members’ whole judgment sets that the members’ judgments on the conclusion neither fix nor need to enter | List & Pettit (2006), LIT-705, read in full in NOTE-550, for the court agenda only. Proposition 1: majority voting on each proposition is not robustly rational, by the discursive dilemma. Proposition 4: the premise-based procedure, majorities on P, Q and the biconditional with R derived, is robustly rational and makes the group’s set a function of the members’ sets. Under it the members’ judgments on R do not fix the group’s (weak discontinuity), and under the distributed procedure they need not enter (strong discontinuity, Proposition 5). The general impossibility for proposition-wise rules is THEORY-127, still Proposed. | Active |
| THEORY-726 | Weight decay on factors is a nuclear-norm penalty on their product: with tied weights λ‖W‖²_F = λ‖WWᵀ‖*, and for untied factors the least (‖U‖²_F + ‖V‖²_F)/2 over UVᵀ = M is ‖M‖*, so for any loss that sees the weights only through the product, square-penalized training is nuclear-norm-penalized training of a product of bounded rank | Boncoraglio et al. (2025), LIT-857, Appendix A, read in NOTE-661, and re-derived here. ‖W‖²_F = Tr(WWᵀ) = ‖WWᵀ‖*, since a PSD matrix’s singular values are its eigenvalues. For untied factors, Hölder’s inequality for Schatten norms and AM–GM bound ‖M‖* by (‖U‖²_F + ‖V‖²_F)/2 over every factorization UVᵀ = M, and the balanced SVD factorization attains it. The product’s rank is bounded by the factors’ inner dimension. It says nothing about what the trained product looks like, which is THEORY-180’s spectral law. | Active |
| THEORY-727 | For a fixed linear operator in an inner-product norm, growth over time t is the top singular value of the propagator, which the eigenvalues bound only from below; it starts at the numerical abscissa, which can be positive when every mode decays; and the forced response is bounded by the condition number of the eigenvectors over the distance to the spectrum | Farrell & Ioannou (1996), LIT-931, read in NOTE-831, with Trefethen et al. (1993), LIT-932, read in NOTE-839. For du/dt = Au with A fixed: a normal A grows as its spectral abscissa; in general the growth over t is σ_max(e^(At)), with the eigenvalues as a floor; the initial growth rate is the top eigenvalue of (A + A†)/2; and harmonic forcing is bounded by κ(E)/dist(iω, Λ(A)), with the ε-pseudospectrum marking where eigenvalues of A + Δ, ‖Δ‖ < ε, can go. All in a chosen norm. The white-noise variance result is THEORY-323’s, still Proposed. | Active |
| THEORY-728 v2 | On a finite data set, a symmetric positive affinity normalized to a Markov operator is conjugate to a symmetric one, and its eigenvectors scaled by powers of their eigenvalues embed the data so that Euclidean distance equals the diffusion distance weighted by the inverse stationary law | Coifman et al. (2005), LIT-981, read in full in NOTE-1441, with the derivation written out here; the 1/π-weighted distance is the companion’s (LIT-1246), not the paper’s own. For n points and a symmetric affinity K with positive entries, A = D⁻¹K is a Markov matrix with stationary law π ∝ d. It is conjugate to the symmetric D^(-1/2) K D^(-1/2), so its eigenvalues are real and in [−1, 1], and in [0, 1] when K is positive semi-definite. The map x ↦ (λ_j^m ψ_j(x))_{j≥1} turns the m-step diffusion distance, weighted by 1/π, into Euclidean distance exactly. Truncation gives a lower bound. It says nothing about the continuum limit, which is THEORY-565. | Active |
| THEORY-729 | An adjunction between a category and the opposite of another restricts to a dual equivalence between the full subcategories on which its unit and counit are isomorphisms | Corfield (2017), LIT-115, §3, read in full in NOTE-141, with the proof the paper omits written out here. For F : C → D^op left adjoint to G : D^op → C, let C′ and D′ be the full subcategories on which the unit and the counit are isomorphisms. Then F and G restrict to inverse equivalences C′ ≃ D′, and D′ is a full subcategory of D^op, so C′ is dually equivalent to a full subcategory of D. Pontrjagin duality is the example. That most dualities are of this form is THEORY-604’s thesis, still Proposed. | Active |
| THEORY-730 | For an embedding whose Gram matrix is the absolute co-occurrence deviation matrix at full rank, words on a periodic lattice whose positive and negative co-occurrence parts each depend only on separation have Fourier modes of the lattice as principal components, in degenerate cos/sin pairs with amplitude the square root of the kernel’s Fourier transform, and the exponential kernel gives a closed loop with integer frequencies on a periodic lattice and an open curve with non-integer frequencies on an interval | Karkada, Korchinski, Nava, Wyart & Bahri (2026), LIT-860, Propositions 1, 3 and 4 and Corollary 2, with the proofs in Appendix E followed in NOTE-664. The result is conditional throughout. It concerns an idealised embedding with W Wᵀ = |M*| and d ≥ rank M*, not a trained one. It needs the positive and negative parts of M* to be translation invariant separately (Assumption B.1), not M* alone. It says nothing about whether any corpus or model satisfies these conditions, which is THEORY-183. | Active |
| THEORY-731 | For softmax cross-entropy with balanced classes, the Gauss–Newton matrix splits exactly into four positive semidefinite second-moment terms, the class-centre term has rank at most C with eigenvectors in the span of the class centres and the spectrum of a C × C Gram matrix, and so the k-th eigenvalue of the whole is never below the k-th eigenvalue of the class-centre term | Papyan (2019), LIT-619, read in NOTE-479. Exact algebra, re-derived here. For softmax cross-entropy, the Gauss–Newton matrix is G = (1/n)ΔΔᵀ, an uncentred second moment of logit derivatives indexed by class and logit. Grouping them gives G = G₀ + G₁ + G₂ + G₃, with every term positive semidefinite. G₁, the class-centre term, has rank at most C, and its spectrum is read from a C × C Gram matrix. So λ_k(G) ≥ λ_k(G₁ + G₂) ≥ λ_k(G₁) for every k, in any network, trained or not. That G₁ carries the outliers of trained networks is measured, not derived, and stays Proposed in THEORY-078. | Active |
| THEORY-732 | For ReLU networks interpolated linearly between two endpoints, weak additivity and commutativity at every layer make each layer’s features exactly the interpolation of the endpoints’ features, output-layer linearity bounds the path’s error by twice the endpoints’, and for one hidden layer with interpolating minima linear mode connectivity alone gives the exact case | Zhou et al. (2023), LIT-674, read in NOTE-512 with Appendix A’s proofs checked: for an L-layer ReLU MLP on a finite dataset, weak additivity of ReLU over the two networks’ pre-activations and the commutativity W_A H_B + W_B H_A = W_A H_A + W_B H_B at every layer make the interpolated network’s features at every layer exactly the interpolation of the endpoints’ features (Theorem 1). Output-layer linearity, at any positive scale, keeps the path’s error within twice the endpoints’ (Lemma 1). Lubana et al. (2022), LIT-669, Lemma 2: for one hidden layer and interpolating minima, linear mode connectivity forces shared activation patterns, and with shared patterns the hidden features are linear along the path. It says nothing about when the conditions hold. That trained pairs satisfy them is THEORY-111’s empirical claim. | Active |
| THEORY-733 | For a stable linear Gaussian VAR(p), a linear coarse-graining is exactly dynamically independent iff its row space is invariant under the transpose of every lag matrix, so for p ≥ 2 almost no parameter set has one at any scale, while for p = 1 they are the transpose’s invariant subspaces, which exist on open sets but not generically at every scale | Barnett and Seth (2023), LIT-979, read in NOTE-791: the VAR form (3.26) of exact dynamical independence, with the genericity count of §3.3 made a proof for VAR order p ≥ 2 and corrected for p = 1. Linear coarse-grainings Y = LX of a stable VAR with non-degenerate Gaussian innovations only. It says nothing about near-independence, about the multimodality of the dynamical-dependence cost, or about nonlinear maps. | Active |
| THEORY-734 | In the hyperbolic plane, a root carrying deg_max ≥ 15 chains of length m, embedded with worst-case distortion 1 + ε for ε ≤ 1, forces some node to hyperbolic distance at least (ℓ/(4ε))·ln(deg_max/(π√2)) from the origin, so fixed-point Poincaré coordinates need Ω((ℓ/ε) log deg_max) bits | Sala, De Sa, Gu and Ré (2018), LIT-874, Lemma D.1, read in NOTE-679, with the proof redone here without the paper’s small-angle approximation. Only the root’s children are used to fix the embedding’s scale c, and then the chains turn the scale into depth. Plane only, one family of trees, fixed-point coordinates in the Poincaré disk, deg_max ≥ 15 and ε ≤ 1. It says nothing about H^r for r > 2, or about whether any tree needs fewer bits under another number system. | Active |
| THEORY-735 | Under a local quadratic model of the loss with the greedy optimal step, per-step progress at batch size B is ΔL_max/(1 + B_noise/B), and at fixed B the steps and examples needed satisfy (S/S_min − 1)(E/E_min − 1) = 1, with E_min/S_min the progress-weighted mean of B_noise | McCandlish, Kaplan, Amodei et al. (2018), LIT-348, §2 and App. D.1, as read and re-derived in NOTE-293. A derivation under stated assumptions: a second-order model of the loss along the step, an unbiased minibatch gradient of covariance Σ/B, and the step size that maximises the expected decrease. It says nothing about whether real training meets those assumptions, or how well the noise scale predicts the measured critical batch, which is THEORY-033. | Active |
| THEORY-736 | Two ε-dropout-stable solutions of a multilayer ReLU net, under a loss convex in the output, are joined by a piecewise-linear path whose loss never exceeds the worse endpoint’s by more than ε, and joined pairwise paths compose with no higher barrier than their worst | Kuditipudi et al. (2019), LIT-671, Theorem 1, read in full in NOTE-544, with Draxler et al.’s (2018) concatenation bound from LIT-653. Dropout stability gives every solution a half-width copy with the same loss up to ε. Half the units are then free, so working units can be swapped in and permuted at no cost. That joins any two such solutions. It is a statement about dropout-stable solutions only: whether training produces them is THEORY-109’s open question, and Theorem 4 of the same paper builds disconnected global minima. | Active |
| THEORY-737 | In a spectral contrastive graph that joins labelled known classes to unlabelled data, the least-squares residual of a novel labelling on the top-k eigenspace, with the labelled entries left free, equals exactly the part of the labelling outside that eigenspace that the labelled rows of the discarded eigenvectors cannot absorb | Sun, Shi, Liang & Li (2023), LIT-235, Theorem 5.5 with its proof in C.1, read in NOTE-833. The paper states the identity as ≤, and its proof is a chain of equalities. Re-derived here in three steps from orthogonality and least squares. With the paper’s Lemma 5.1 it bounds the novel labelling’s 0–1 linear-probe error by twice this residual. It is about the exact rank-k factorization of a population graph, not about trained networks. | Active |
| THEORY-738 | In the unconstrained-features max-margin problem with k classes under step imbalance and feature dimension at least k − 1, the unique optimal logits are the simplex-encoded labels, every margin equals one, and the classifier and embedding Gram matrices are the two square-root factors of that matrix’s singular value decomposition; the geometry is the simplex equiangular tight frame exactly when the classes are balanced or there are two of them | Thrampoulidis, Kini, Vakilian and Behnia (2022), LIT-994, Theorem 1 and Corollary 1.3, read in NOTE-764 and re-derived here. By THEORY-726 the problem is nuclear-norm minimisation of the logits under margin constraints. The polar factor of the simplex-encoded label matrix certifies it optimal, because under step imbalance its off-diagonal entries are negative. It does not say that gradient descent or trained networks reach this geometry, which is THEORY-286’s. | Active |
| THEORY-739 | For the quartic proxy of word2vec with tied weights, symmetric reweighting and constant weights, the rank-d minimisers are the top d eigenvectors of the relative deviation-from-independence matrix M*, scaled by the square roots of their eigenvalues, up to rotation; and from an initialisation aligned with those eigenvectors, gradient flow acquires each one in an independent logistic rise, in order of eigenvalue | Karkada, Simon, Bahri and DeWeese (2025), LIT-855, Theorem 1 and Proposition 2, read in NOTE-660 and re-derived here. The quartic proxy is a function of WWᵀ alone, so von Neumann’s trace inequality gives its rank-d minimisers. Gradient flow from an aligned start keeps the eigenbasis and reduces each mode to a logistic equation. It does not say that word2vec, or the proxy from random initialisation, behaves this way; that is THEORY-182’s. | Active |
| THEORY-740 | A two-layer linear network trained by gradient flow on white inputs from a decoupled, balanced start learns each singular mode of its input–output correlation in a logistic rise that waits a time of order its inverse strength times the log of the inverse initial scale, so the modes arrive one at a time in order of strength; a single-layer network on the same data learns every mode on one timescale with no plateau, so under these conditions the stages come from the product of layers and the data’s spectrum | Saxe, McClelland and Ganguli (2014, 2019), LIT-864 and LIT-862, read in NOTE-667 and NOTE-666, re-derived here. From a decoupled, balanced start the two-layer equations keep the SVD basis of Σyx, and each mode’s strength obeys τȧ = 2a(s − a), a logistic rise. One weight matrix on the same data relaxes every mode exponentially on the one timescale τ. It does not say that random starts follow the solution, which is THEORY-186’s. | Active |
| THEORY-741 | A two-layer ReLU student of width at least kM, fitting an orthonormal teacher of M neurons on the sphere, has for any k global minima a global minimum joined to each by a two-piece linear path of minima; and in a deep linear network of depth L and width above 1 + r(L − 1), any r global minima in general position share a global minimum linearly connected to each | Lin, Li and Wu (2024), LIT-682, Theorems 6, 11 and 18 with Lemmas 7 and 25, read in NOTE-535 and re-derived by the promotion audit. Two toy models whose minima can be written down: a two-layer ReLU student of an orthonormal teacher on the sphere at population loss, and a deep linear network fitting y = Qx. Spare width lets every minimum be moved, along segments of minima, to one a common centre can reach. No permutation symmetry is used, and nothing is claimed about trained networks. | Active |
| THEORY-742 v2 | For a Boltzmann distribution linear in its couplings, observed through any coarse-graining map, the Fisher information the coarse data lose about the bare couplings is the expected conditional covariance of the energy operators given the coarse state; when the renormalized Hamiltonian stays in the family, the parameter map is linear and the additive constant of the step is analytic, that loss is the constant’s Hessian, so the singular part of the metric passes unchanged to the coarse data. In the hopping model of diffusion at its Gaussian fixed point, keeping every n-th position of a trajectory of fixed duration multiplies the metric by n^(1−μ) in the μ-th Hermite coordinate: the drift’s information is kept exactly, the variance’s falls as 1/n, and higher shape parameters’ faster | Raju, Machta and Sethna (2018), LIT-1254, read in NOTE-972. The loss identity holds for any coarse-graining of an exponential family; that the loss is analytic, and so spares the singular part of the metric, needs an exact renormalization step with linear beta functions and an analytic constant. It does not say that relevant directions keep their information in general: on the paper’s own scalings only directions with RG eigenvalue above d/2 do, and away from the Gaussian fixed point even the drift loses information. | Active |
| THEORY-743 | For finite X and Y, every information-bottleneck optimum at every β gives one encoder to all inputs sharing p(y|x), so it is a stochastic coarsening of the minimal sufficient partition (the causal states of memoryless transduction); as β → ∞ the optima converge to that partition, but in general no finite β attains it, except when Y is a function of X | Shalizi and Crutchfield (LIT-1240, read in NOTE-976) assert that the information bottleneck recovers the causal states as β → ∞. The record proves it, against stochastic encoders as well as partitions, and adds that every finite-β optimum factors through those states. So the IB hierarchy always nests under its top. It says nothing about whether optima at two finite β nest. Finite alphabets only. | Active |
| THEORY-744 v2 | As the kernel width ε goes to 0, Coifman and Lafon’s α-normalized diffusion operator (I − P_{ε,α})/ε, for data sampled with density q = e^{−U} from a compact manifold without boundary, converges uniformly on smooth functions, at rate O(ε), to Δf + 2(1 − α)⟨∇U, ∇f⟩ with Δ the non-negative Laplace–Beltrami operator, which is minus the generator of a reversible diffusion with drift −2(1 − α)∇U and invariant density proportional to q^{2(1−α)}; α = 0 gives potential 2U and invariant density q², α = 1/2 gives the Langevin dynamics whose invariant density is the sampling density itself, and α = 1 gives Brownian motion on the manifold, with no trace of the density | Coifman and Lafon (2006), LIT-1246, read in NOTE-985, with the PNAS announcement LIT-981. The paper states the limit as a Schrödinger operator. Written as a drift, it shows what each α keeps of the density: the walk’s stationary density is q^{2(1−α)}. On a manifold without boundary the limit is derived in full, the kernel expansion included (re-derived on promotion, 2026-10-20). The paper’s own α = 1/2 display has a sign error. Its boundary rate and heat-kernel proof are incomplete and are left to QUESTION-231. | Active |
| THEORY-745 | For the reversible walk p = k/d built from a symmetric non-negative kernel on a finite connected set, the t-step diffusion distance is exactly the Euclidean distance between the coordinates λ_l^t ψ_l, and keeping only the coordinates with |λ_l|^t > δ|λ₁|^t errs in D_t² by at most δ²|λ₁|^{2t}(1/π(x) + 1/π(y)), an absolute bound and not the relative accuracy δ that Coifman and Lafon state; the truncated maps are nested as t grows, so with δ fixed the steps t order a refinement chain by eigenvalue modulus, while untruncated they are all invertible images of one another | Coifman and Lafon (2006), LIT-1246, read in full in NOTE-985. The identity D_t² = Σ λ_l^{2t}(ψ_l(x) − ψ_l(y))² is exact. The paper’s Proposition 1 says the truncated map keeps it “up to relative accuracy δ”. The true bound is absolute and can be large relative to D_t for nearby points. In the refinement sense, the diffusion-map family coarsens with t only through the threshold. Finite sets, counting measure and reversible walks only. It says nothing about the manifold limit or about non-reversible chains. | Active |
| THEORY-746 | Over a fixed finite set of basis functions, slow feature analysis is a generalized eigenproblem: the outputs that minimize ⟨ẏ²⟩ under zero mean, unit variance and decorrelation are the bottom generalized eigenvectors of the derivative covariance against the covariance, in order of slowness, and a stack of such stages, each of whose function spaces contains its inputs, can only keep or lower each of its first m slowness values on the training signal, and may keep them | Wiskott and Sejnowski (2002), LIT-1249, read in full in NOTE-971. Within the span of a fixed basis, the slowest decorrelated unit-variance outputs are the bottom generalized eigenvectors of the pencil (⟨ż̃ż̃ᵀ⟩, cov z̃), and each output’s slowness is its eigenvalue. A consequence the paper does not draw: a stack of such stages whose function spaces contain their inputs is never faster at a higher stage, componentwise, on the training signal, so in this model “higher is slower” is imposed by the objective, weakly, and can stall. It is about the training signal and a fixed function space. It says nothing about test data, about a generative model, about invariance as opposed to slowness, or about learning dynamics. | Active |
| THEORY-747 | In Fourier–Galerkin large-eddy simulation, a first-order finite-memory Mori–Zwanzig closure tracks filtered-DNS energy decay and dissipation on the viscous Burgers equation and on the incompressible Taylor–Green vortex, isotropic turbulence and channel flow about as well as dynamic Smagorinsky where that model is at home and better than Smagorinsky and the t-model on the transitional Taylor–Green vortex; the memory length that fits it is set by the cutoff, not by the flow alone, scaling in Burgers roughly as 0.2 over the spectral radius of the resolved variables’ Jacobian | Parish and Duraisamy (2017), LIT-1259, read in NOTE-973. The closure is THEORY-760’s finite Markovian augmentation. Here is how it did, as far as the paper’s plots show: close to filtered DNS in integral quantities, comparable to dynamic Smagorinsky in equilibrium turbulence, clearly better on a transitional flow, and with the subgrid transfer peaked at the cutoff where DNS puts it but about 40% too deep. The paper calls the predictions “excellent” with no numbers. Its fitted memory length shortens as the resolved dynamics speed up, so the memory belongs to the cutoff as much as to the flow. | Proposed |
| THEORY-748 | Block entropies, and so every lag-τ entropy rate of a stationary signal, are unchanged by the reflection x → −x and by time reversal, so they cannot detect the odd-order asymmetry the 4/5 law ties to energy flux; Granero-Belinchón, Roux and Garnier’s entropy rate conditioned on the sign of the increment breaks the reflection invariance, but h⁺ ≠ h⁻ shows only that the two-point distribution lacks central symmetry, which a skewed one-point distribution produces with exactly symmetric increments, so the test does not by itself detect skewed increments or an energy cascade | Granero-Belinchón, Roux and Garnier (2016), LIT-1243, read in NOTE-970, claim that conditioning the entropy rate on the sign of the increment lets one “prove the existence of the energy cascade” using information theory. The record finds two limits. The unconditioned entropy rate is exactly blind to reflection and time reversal. The conditioned one detects any central asymmetry of the two-point law, including one with no increment skewness at all. Independent pairs with the paper’s one-point skewness of 0.175 give h⁺ − h⁻ ≈ 0.066 nats with symmetric increments. Nothing in the paper ties an information quantity to the energy balance. | Active |
| THEORY-749 v3 | A weak solution of the incompressible Euler equations on the periodic box that lies in L³(0,T; B^α_{3,∞}) ∩ C([0,T]; L²) with α > 1/3 conserves kinetic energy, because the energy flux into scales below a mollification scale ε is bounded by Cε^(3α−1)∫‖u‖³ and so vanishes as ε → 0; this does not show that rougher solutions dissipate | Constantin, E and Titi (1994), LIT-1248, read in NOTE-982. The positive half of Onsager’s conjecture, in the Besov form: if velocity increments obey ‖u(·+y) − u‖_{L³} ≤ C|y|^α with α > 1/3, integrated in time, the coarse-grained energy flux across scale ε is O(ε^(3α−1)) and no energy can be lost to vanishing scales. It is a statement about regular fields only. It does not show that a flux survives the limit for rougher ones: that energy can fail to be conserved below 1/3 is Isett’s later theorem (THEORY-763), that it can strictly decrease is Buckmaster, De Lellis, Székelyhidi and Vicol’s (THEORY-776), both Proposed, and some rough solutions conserve energy anyway. | Active |
| THEORY-750 | For a stationary Gaussian signal the lag-τ entropy rate with one-point embedding is h_τ = H(X) + ½ log(1 − c(τ)²), so where the normalized second-order structure function 1 − c(τ) is small and scales as τ^ζ₂, h_τ = (ζ₂/2) log τ + constant; the “scaling of information” that Granero-Belinchón, Roux and Garnier measure in near-Gaussian wind-tunnel turbulence, slope 1/3 in the inertial range and 1 in the dissipative range, is the scaling of the second-order structure function written in nats | Granero-Belinchón, Roux and Garnier (2016), LIT-1243, read in full in NOTE-970. A Gaussian identity and its small-lag asymptotics: the conditional entropy of x(t) given x(t − τ) is a monotone function of the autocorrelation, so its scaling exponent is half the structure-function exponent. In the Modane data the estimated entropy rate matches the Gaussian formula, so the measured “information spectrum” is S₂ again. It is not a distribution of a conserved quantity over scales, and it carries nothing about the direction or size of energy transfer. It answers QUESTION-219 only in the narrow sense of supporting A3’s caution. | Active |
| THEORY-751 v2 | For a memoryless source with finite alphabets and a per-letter distortion, a description at rate R(D₁) can be refined to distortion D₂ < D₁ at total rate R(D₂) iff some pair of rate–distortion-optimal test channels forms a Markov chain X → X̂₂ → X̂₁; the condition holds for every discrete source under Hamming distortion and fails for some three-letter sources under absolute error | Equitz and Cover (1991), LIT-1238, read in NOTE-988, with every step re-derived by 2026-10-20. Lossless two-stage description is possible exactly when the coarse optimum is a stochastic degradation of the fine optimum. That is a Markov chain on test channels, not nesting of partitions, and it is an asymptotic block-coding statement. It does not say that optimal single-shot quantizers or deterministic encoders nest, and the paper’s own Gaussian example shows they need not. It says nothing yet about the information bottleneck beyond a formal transfer through the KL distortion. | Active |
| THEORY-752 | In optimal prediction of a Hamiltonian system with separable energy and canonical initial law, projected by conditional expectation, the t-model’s leading-order memory term tPLQLx makes the effective Hamiltonian of the resolved variables non-increasing, so the eliminated variables’ memory enters as a damping that grows linearly in time | Chorin, Hald and Kupferman (2002), LIT-1253, read in NOTE-975: Theorem 8.1. Truncating the Mori–Zwanzig memory integral at its lag-zero value gives dΦ/dt = R̄(Φ) + tS(Φ), and under the stated conditions this dissipates the free energy of the resolved variables. It says nothing about how well the t-model predicts, gives no error bound, and holds only for the conditional-expectation projection; the true conditional mean’s effective energy need not decrease. | Active |
| THEORY-753 | For finite X and Y, the information bottleneck is successively refinable from budget λ₁ to λ₂ > λ₁ iff some pair of optimal encoders forms a Markov chain X → T₂ → T₁, that is, iff the coarse optimal encoder is a garbling of a fine one; when the fine optimum’s decoder points q(X|t₂) are affinely independent, this holds for that pair iff every decoder point q(X|t₁) of the coarse optimum lies in their convex hull, so a failed hull test on optima that are unique up to merging and relabelling proves that refinement fails | Charvin, Catenacci Volpi and Polani (2023), LIT-1258, read in NOTE-981. It turns QUESTION-220’s Markov formulation into a finite check: nesting between two IB optima is a convex-hull inclusion of their decoder points, which a linear programme decides. The check is on given optima, and refinability asks for some pair. So a failed check settles the question only when the optima are certified globally optimal and unique. This entry adds that the information bottleneck’s own convex-envelope dual can supply that certificate. Finite alphabets, two stages. | Active |
| THEORY-754 v2 | If a velocity field’s third-order increments obey ‖δu(r)‖₃ ≤ C u_rms (r/L)^σ at every separation r, with 0 < σ < 1, then for a smooth, rapidly decaying filter the space-averaged energy flux across scale ℓ takes at most a fraction of order (ℓ/Δ)^(1−σ) from strain at scales above Δ and of order (δ/ℓ)^(2σ) from stress at scales below δ, measured against u_rms³/L·(ℓ/L)^(3σ−1); so transfer between scales is local in scale, with a power-law decay and no gap | Eyink and Aluie (2009), LIT-1239, read in NOTE-969, stating bounds proved in Eyink (2005), LIT-1252. A conditional inequality: if velocity increments scale no faster than r^σ in the L³ mean, the contributions of far larger and far smaller scales to the mean flux across ℓ are bounded by powers of the scale ratio. It needs 0 < σ < 1: σ < 1 for the large scales, σ > 0 for the small. That the inertial range satisfies the hypothesis, that the mean flux there is non-zero, and the sharper 4/3 exponent are assumptions or heuristics, not part of it. It is about one field decomposed by scale, and says nothing about units. | Active |
| THEORY-755 v3 | For a linear system x(t+1) = Ax and a partition of its variables, the vector of block sums evolves autonomously from every initial state iff the partition is column-equitable, every column of each block of A summing to the same value; the aggregate operator then keeps a subset of A’s eigenvalues, and the blocks may interact as strongly as they like, so exact aggregation is not decomposition | Shpak, Stadler, Wagner and Hermisson (2004), LIT-1242, read in NOTE-979. Exact aggregation of a linear system by the sums over a partition holds for every state iff the partition is column-equitable, a symmetry condition, not a weak-coupling one. Linear dynamics and partition-based aggregation only. It says nothing about approximate aggregation, the Simon–Ando case, or nonlinear systems, where the paper itself shows aggregations with no linear counterpart. | Active |
| THEORY-756 | The growth rate of thermodynamic depth is the entropy rate of whichever macrostate process it is computed over, so the choice of macrostates sets it anywhere from zero up; among partitions of a stationary process’s past that predict every finite stretch of the future as well as the whole past does, the causal states are the coarsest, so they have the least entropy and the least entropy rate | Crutchfield and Shalizi (1999; arXiv 1998), LIT-1260, read in NOTE-978. Depth is not a structure measure until its states are fixed. Predictive sufficiency, then minimality, fixes them as the causal states. The choice is canonical only given the measuring instrument and the target, the observed future. The redefined dive is still an entropy rate. | Active |
| THEORY-757 | The information bottleneck is successively refinable between every pair of budgets when Y is a function of X, by nested erasures of Y, and when X and Y are both binary, where the optimum at each nonzero budget is unique up to merging and relabelling and its two decoder points are the ends of an interval of the source simplex that only widens as the budget grows | Charvin, Catenacci Volpi and Polani (2023), LIT-1258, read in NOTE-981. These are the two finite cases in which nested information-bottleneck optima are guaranteed at every pair of budgets. Neither reaches the record’s four-state source, whose Y is not a function of X and whose X has three effective states. NOTE-981 finds that source not refinable. So binary Y alone does not guarantee nesting. The function case is the degenerate one, where the bottleneck is just a noisy copy of Y. | Active |
| THEORY-758 | For a self-adjoint diffusion operator T with spectrum in [0, 1], the diffusion-wavelet levels are spectral subspaces spanned by the eigenvectors with λ^s ≥ ε for an increasing sequence of powers s, so they form an exactly nested chain of T-invariant subspaces whose differences are bands of the spectrum, about one octave each, not spatial blocks; Coifman and Maggioni’s compressed algorithm, which squares the operator on each orthonormal basis, thresholds T^{2^{j−1}} at level j and not T^{2^j−1} as the paper states; and since each level is T-invariant, each is an exactly closed linear coarse-graining whose localized basis is a choice the level does not fix | Coifman and Maggioni (2006), LIT-1256, read in full in NOTE-984. The levels of a diffusion multiresolution are spectral bands. Nesting is exact and needs no decay of the spectrum, and decay buys only compression. The compressed algorithm as written keeps ⟨ξ : λ^{2^{j−1}} > ε⟩ at level j, and the paper’s own Fig. 9 follows this, not its stated count. Each level closes exactly under T, but a single scaling function does not. It says nothing about non-self-adjoint operators, about error bounds for the compressed scheme with finite precision, or about when a localized basis exists. | Active |
| THEORY-759 | A six-layer, 256-unit ReLU network trained by full-batch Adam to regress a sum of sinusoids at 5 to 50 cycles on [0, 1] fits the components in order of frequency, and keeps that order when the amplitudes rise tenfold with frequency, so in this setting the order of acquisition is set by the learner and not by the strength of the target’s components | Rahaman et al. (2019), LIT-1261, Experiment 1, read in full in NOTE-983. With equal amplitudes, and with amplitudes rising from 0.1 at 5 cycles to 1 at 50, the normalised fit |f̃(k_i)|/A_i reaches 1 at low frequency first. This is the reverse of the order by strength that THEORY-186 gives for a deep linear network. One architecture, one optimiser, a 1-D input, ten runs averaged. The paper’s theory gives a bound on speed, not this order. | Proposed |
| THEORY-760 | The finite-memory Mori–Zwanzig closure that Parish and Duraisamy take from Stinis, truncated at order m with one trapezoidal sub-interval and constant memory lengths, is a finite-dimensional Markovian augmentation: m + 1 auxiliary variables per resolved mode, each relaxing at rate 2/τ; at first order it replaces the memory integral by the kernel 2e^{−2s/τ₀} acting on the first-order term, which tends to τ₀ times that term, the t-model with t replaced by τ₀, when τ₀ is short against the resolved dynamics; its kernel is twice the true one at zero lag for every τ₀, so it is not exact even where the true memory is a single exponential, and nothing in the construction bounds its error | Parish and Duraisamy (2017), LIT-1259, read in NOTE-973. The finite-memory closure turns the Mori–Zwanzig memory integral into auxiliary ordinary differential equations, so the reduced model is the resolved variables plus finitely many memory coordinates: the shape of augmentation QUESTION-222 asks about. But the truncation drops the next auxiliary term without a bound, the memory length is fitted, and the kernel’s form is fixed by the quadrature, not by the eliminated dynamics. It is an augmentation with uncontrolled error, not the controlled one the question asks for. | Active |
| THEORY-761 | A continuous piecewise-linear function on R^d with compact support has a Fourier transform that, along any fixed direction û, is bounded by C(û)k^(−2), and by C(û)k^(−d−1) whenever û is orthogonal to no edge of its linear regions, which is almost every direction; C(û) is not uniform and grows without bound near the exceptional directions; for a ReLU network without compact support the statement is not established | Rahaman et al. (2019), LIT-1261, read in full in NOTE-983. One integration by parts turns f̃ into a sum of polytope transforms weighted by the region gradients and divided by k. Each further step of Diaz et al.’s recursion gains another 1/k until the path reaches a face whose directions are all orthogonal to k. Generic directions reach the vertices, giving k^(−d−1), and every direction gets at least k^(−2). It is a bound on what a piecewise-linear function contains, not a statement about training. Unbounded ReLU networks fall outside it. | Active |
| THEORY-762 | For a reversible diffusion dX = −∇U dt + √2 dW in equilibrium, an eigenfunction ψ of its generator with eigenvalue −λ is closed in conditional mean with no memory: E[ψ(X_{t+s}) | the whole past] = e^{−λs}ψ(X_t), and so the same given ψ’s own past; but ψ(X_t) is a Markov process in its own right only when |∇ψ|² is a function of ψ, since otherwise its own path reveals a noise intensity that its present value does not fix | The record’s answer to what Nadler et al. (LIT-1250, read in NOTE-986) leave implicit when they call slow eigenfunctions reaction coordinates. Such a coordinate is exactly closed in its mean: its best prediction from the full state and from its own history coincide, with no memory term, and the Mori–Zwanzig memory and noise for it vanish under Mori’s projection. It is closed in law only under a further condition. In the paper’s examples the condition holds; the mixed Ornstein–Uhlenbeck eigenfunction x₁x₂ shows it can fail. This does not say that diffusion maps estimate the eigenfunctions well from finite data, or that a slow eigenfunction is the best coarse variable. | Active |
| THEORY-763 v2 | For every α < 1/3 there is a nonzero weak solution of the 3D incompressible Euler equations on the periodic box, with velocity Hölder-continuous of exponent α in space and time, that vanishes outside a finite time interval; its energy is not conserved, so the energy flux across a mollification scale ε does not vanish as ε → 0, and it runs in both directions, out of the vanishing scales while the energy rises and into them while it falls | Isett (2018), LIT-1255, skimmed in NOTE-974: the negative half of Onsager’s conjecture. With THEORY-749 (Constantin, E and Titi, the positive half) it makes 1/3 the threshold. For the record, its point is that below 1/3 the energy flux into vanishing scales can survive the limit, which is the half of A3’s point that THEORY-749 could not give. It does not say that this flux is a dissipative cascade. Isett’s solutions start from rest, gain energy and lose it again, so the surviving flux takes both signs. Nor does it say that such solutions are limits of Navier–Stokes or describe turbulence. | Proposed |
| THEORY-764 | For a deterministic supervenient feature V of a Markov system, Rosas et al.’s practical emergence criterion Ψ equals the parts’ whole-minus-sum information about V’s next value minus V’s one-step dynamical dependence I(V_t′; X_t | V_t), so dynamical independence raises Ψ but neither implies emergence nor is implied by it, and the paper’s sufficient test for causal decoupling can pass a feature that is not dynamically independent | Rosas et al. (2020), LIT-1244, read in NOTE-987, with Barnett and Seth’s dynamical independence (LIT-979, THEORY-257). By the chain rule, Ψ(V) = [I(X_t;V_t′) − Σ_j I(Xʲ_t;V_t′)] − I(V_t′;X_t|V_t). The subtracted term vanishing implies Barnett–Seth independence for Markov X. Examples show each condition without the other. The independent sum of AR(1) channels has both, with no interaction. The identity concerns Ψ, the paper’s practical criterion; it says nothing about the PID quantities themselves. | Active |
| THEORY-765 v2 | Brushing a seen rubber hand in synchrony with the hidden real hand makes touch be felt at the rubber hand, makes it be reported as one’s own, and shifts the felt position of the real hand toward it; a small asynchrony removes these effects | Botvinick & Cohen (1998), LIT-1277, read in full in NOTE-1006. Ten subjects affirmed referred touch and ownership after ten minutes of synchronous brushing; after thirty minutes their blind reaches drifted toward the rubber hand in proportion to how long the illusion was reported; asynchronous brushing cut both. It does not show that synchrony alone, apart from expectation, produces the report, and it concerns a hand, not the whole body or the self. | Rejected — Rejected on 2026-10-20 by its own refutation condition: drift toward the rubber hand appeared as strongly under asynchronous brushing interrupted by pauses, and with the hand only seen (Rohde et al. 2011, LIT-1281). Its suggestion control was also too weak to separate perception from expectation (Lush & Seth 2022, LIT-1267). The report half is restated, narrower, in THEORY-766. |
| THEORY-766 v2 | Brushing a seen rubber hand in synchrony with the hidden real hand, against asynchronous brushing, raises reports that touch is felt at the rubber hand and, more weakly and less reliably, that the rubber hand is one’s own; the proprioceptive drift toward the rubber hand that accompanies these reports is not a measure of them; the standard comparison conditions do not equalise participants’ expectations, so whether the stimulation or the expectation produces the report difference is open | Botvinick & Cohen (1998) and four replications read here give a synchrony effect on reports of referred touch and ownership. Rohde et al. (2011) and Abdulkarim & Ehrsson (2016) separate drift from ownership. The suggestion debate (Lush 2020; Lush et al. 2020; Ehrsson et al. 2022; Lush & Seth 2022; Roseboom & Lush 2022) shows that the standard controls do not equalise expectations. The ownership report is weaker than the referred-touch report and tracks trait suggestibility. Whether the synchronous stimulation, not expectation, produces the report difference is not settled. Promoted 2026-10-20 on the report differences measured (ADR-047 v3); the perceptual reading is THEORY-827. | Active |
| THEORY-767 v2 | Body ownership draws on interoceptive as well as exteroceptive signals: a visual cue synchronous with one’s heartbeat increases ownership of a virtual hand and identification with a virtual body, and lower interoceptive sensitivity goes with greater susceptibility to the rubber hand illusion | Seth (2013), LIT-1263, read in full in NOTE-1000. An opinion article that reports, at second hand, that a virtual hand pulsing with the heartbeat was owned more (Suzuki et al. 2013, the author’s own group), that a virtual body pulsing with it was identified with more (Aspell et al. 2013), and that people with lower heartbeat-detection sensitivity are more susceptible to the rubber hand illusion (Tsakiris et al. 2011). None of the studies was read here, and no control separates the heartbeat from any other periodic signal. | Proposed |
| THEORY-768 v2 | Minimal selfhood is identification with the whole body, located where that body is felt to be and seen from inside it; owning a body part does not reach it, and bodily agency enables it causally without being part of it | Blanke & Metzinger (2009), LIT-1274, read in full in NOTE-1002, with Lenggenhager et al. (2007), LIT-1279, read in full in NOTE-999, for the full-body illusion it leans on. Minimal phenomenal selfhood is given three dimensions: global self-identification, self-location and a weak first-person perspective. Out-of-body experience, heautoscopy and full-body illusions vary them; the rubber hand illusion is said not to. The necessity and sufficiency claims are asserted, and the agency thesis rests on adults whose agency was intact. | Proposed |
| THEORY-769 v2 | Ownership of a body part is a graded belief that it is the most probable common cause of correlated multisensory input, so that synchronous stimulation of another object moves some of that belief to the object and away from the real part | Apps & Tsakiris (2014), LIT-1262, read in full in NOTE-991, with Botvinick & Cohen (1998), LIT-1277, for the illusion it explains. The rubber hand, enfacement and rubber-voice illusions are read as one inference: unimodal surprise from synchronous stimulation is explained away by shifting the probability that a part is “me”. The account fits the findings; its authors grant there is little direct evidence and that it is hard to falsify with standard fMRI. It does not say why such a model is experienced as a self. | Proposed |
| THEORY-770 | In a closed population, any mapping of ancestors to descendants gives the Price equation: mean fitness times the change in mean character equals the covariance of fitness and character plus the fitness-weighted mean of the change in character, over any time interval and with no assumption beyond closure | Luque (2016), LIT-205, §3, read in NOTE-101, after Price (1970); the derivation re-derived by the promotion audit. An identity, not a model: it says nothing about which partition of the change a causal model licenses, predicts nothing until fitness and transmission are specified, and fails without closure (migration). | Active |
| THEORY-771 v4 | In a singularly perturbed system, fast states x̃ with dx̃/dt = f̃(x̃, y) + ε·δf and slow states y with dy/dt = ε·ḡ(y) + ε·δg, if f̃ is contracting in x̃ at rate β_f with x̃ = 0 an equilibrium for every y, ḡ is contracting at rate β_g, and |δf| ≤ d_f + α_f,x|x̃| + α_f,y|y|, |δg| ≤ d_g + α_g,x|x̃|, then for every ε below ε_c = β_f / [χ_f(α_f,x + χ_g α_f,y α_g,x / β_g)] the fast states stay within O(ε) of zero and, when d_g = 0, the slow states within O(ε) of the reduced trajectory, uniformly in time after a transient of order (1/β_f + 1/(εβ_g)) log(1/ε) | Bousquet and Slotine (arXiv 2015), LIT-1292, read in NOTE-1025. It gives Simon’s near-decomposability the rate in ε that THEORY-661’s open statement lacks: first order, for trajectory error, uniform in time, under contraction of the modules and of the reduced slow system, with an explicit, sufficient ceiling on ε. Deterministic. It bounds how far the states are from the reduced description, not how much information the rest of the system sends into the slow variables, and it takes the slow coordinates as given. | Active |
| THEORY-772 v2 | For every β < 1/3 there is a weak solution of the 3D incompressible Euler equations on the periodic box, in C⁰_t(B^β_{3,∞} ∩ L^{1/(1−3β)}), whose Duchon–Robert dissipation is the smooth nonnegative density E(t, x) = −e(t)e′(t)ρ₀(x₁, x₂)² fixed at the construction’s first step; for such a solution the local coarse-grained energy flux into scales below ℓ converges, as ℓ → 0 and as a distribution in space and time, to E, so the transfer into vanishing scales is one-way at every place and time in the limit, nonzero inside a periodic array of pipes and zero outside them; where and how fast energy is dissipated is chosen by the construction, not forced by the equations, and nothing is shown about the sign at any positive scale | Giri, Kwon and Novack (2023; Annals 2026), LIT-1289, skimmed in NOTE-1022: the L³-based strong Onsager theorem. Below 1/3, in Constantin, E and Titi’s own scale of spaces (THEORY-749), there are weak Euler solutions satisfying the local energy inequality. In the proof the Duchon–Robert measure is a prescribed smooth function, positive in a periodic array of pipes and zero elsewhere. So the coarse-grained flux into vanishing scales is one-signed locally in space and time, in the limit, and not only for the whole box as in THEORY-776. Its location and rate are inputs of the construction; it is a smooth density on a few pipes, not concentrated on a thin set; nothing is said about the sign at a positive scale or about vanishing viscosity. | Proposed |
| THEORY-773 v2 | In a singularly perturbed system ẋ = f(x, z, t), εż = g(x, z, ε), if g is contracting in z at rate λ_z for every x and ε, the reduced system ẋ = f(x, γ(x), t) on the slow manifold z = γ(x) is contracting at rate λ_x, f is α-Lipschitz in z, |∂γ/∂x · f| ≤ d and g is K-Lipschitz in ε, then for all t ≥ 0 the fast state is within χ_z e^{−λ_z t/ε}|z(0) − γ(x(0))| + εχ_z(d + K)/λ_z of the manifold and the slow state within χ_x|x(0) − x_γ(0)|e^{−λ_x t} + ε[C₁(e^{−λ_x t} − e^{−λ_z t/ε}) + C₂(1 − e^{−λ_x t})] of the reduced trajectory; partial contraction of f in x alone is not enough | Del Vecchio and Slotine (IEEE TAC 2013), LIT-1295, read in NOTE-1020, with their Theorem 3’s hypothesis corrected. A global, uniform-in-time, first-order bound on the error of the quasi-steady-state reduction, with every constant explicit and no requirement that ε be small. The reduction is Markovian: eliminating a fast, contracting variable costs O(ε) in trajectory error for all time, so no memory term is needed to that order. Constant metrics, deterministic, and the bound d on how fast the manifold moves is needed along the trajectory. | Active |
| THEORY-774 | In a one-dimensional lattice hopping model with 2N+1 free hopping probabilities, all particles starting at the origin and the density after t steps observed with fixed Gaussian error, the Fisher metric is exactly t² times the distribution of the difference of two independent (t−1)-step walks, evaluated at the lag between the two hops, so it does not depend on the drift; when the walk is aperiodic with nonzero variance, its k-th largest eigenvalue is of order t^(3/2−k) for k = 0, …, 2N, so successive eigenvalues separate by a factor of order t | Machta, Chachra, Transtrum and Sethna (2013), LIT-1299, supplement §III, read in NOTE-1018. The eigenvalues grow for particle creation (t^(3/2)) and drift (t^(1/2)) and fall from the diffusion constant on (t^(−1/2), t^(−3/2), …). The data are not a coarse-graining of one fixed data set, so nothing forbids growth. The metric is a least-squares metric with an arbitrary unit of error, and its eigenvalues depend on the coordinates θ_μ. The ratio between successive eigenvalues matches the 1/n per Hermite order of THEORY-742’s diffusion result, though the two set-ups differ. | Active |
| THEORY-775 | With a Gaussian random-walk prior and an instantaneous unit-variance Gaussian encoder, the KL half of the evidence lower bound is the unordered slowness loss plus a constant; with a linear Gaussian encoder and decoder on whitened input, the bound is maximized on the span of the slowest SFA directions whose lag-one autocorrelation exceeds one half, with the basis inside that span unidentified, and on unwhitened input the maximizer is neither SFA’s subspace nor invariant to rescaling the input | Schüler and Wiskott (2025), LIT-1296, read in full in NOTE-1015. The ELBO of a dynamical VAE with prior N(z_{t−1}, I) and encoder N(g(x_t), I) is Σ E log p(x_t | z_t) − ½Σ‖g(x_{t−1}) − g(x_t)‖² − (T − 1)d/2, an exact identity. For linear Gaussian encoder and decoder on whitened input, the maximizer spans the bottom eigenvectors of the difference covariance with eigenvalue μ < 1, each scaled by (μ^{−1/2} − 1)^{1/2} and then rotated arbitrarily. So it recovers SFA’s slow span, cut at lag-one autocorrelation ½, not SFA’s features. On raw input it trades variance against slowness. It says nothing about nonlinear encoders, about predictive sufficiency, or about Turner and Sahani’s model. | Active |
| THEORY-776 v3 | For every β < 1/3 and every smooth, strictly positive and strictly decreasing energy profile e(t) on [0, T], there is a weak solution of the 3D incompressible Euler equations on the periodic box, Hölder-continuous of exponent β in space and time, with ∫|v(t)|² = e(t) at every time; for such a solution the energy flux across a mollification scale ε, integrated over any time interval, tends as ε → 0 to ½ times the drop in e, which is strictly negative, so energy leaves the resolved field for vanishing scales on every interval; this is one-way for the energy of the whole box, not at every point, and it is chosen by the prescribed profile, not forced by the equations | Buckmaster, De Lellis, Székelyhidi and Vicol (2017; CPAM 2019), LIT-1300, read in NOTE-1013: the admissible version of Isett’s negative half of Onsager’s conjecture (THEORY-763). Any smooth positive energy profile can be imposed on a C^β solution, β < 1/3, so a strictly decreasing one gives solutions whose total energy only falls. Through THEORY-749’s energy balance, the coarse-grained flux then runs into the vanishing scales on every time interval. That is the one-way transfer THEORY-763 could not give. It is one-way for the box as a whole, not at every point (no local energy inequality is proved); the same theorem gives increasing energy as readily, so the direction is a choice of the construction; and nothing ties these solutions to Navier–Stokes, to a constant-flux inertial range or to uniqueness. | Proposed |
| THEORY-777 | In Monte Carlo on a 64×64 periodic square-lattice Ising model at its critical point, parametrized by a field and 13 nearby couplings and observed only through the spins left after n checkerboard decimations (b = √2 per step, n ≤ 6), the two Fisher eigenvalues along the field and the gradient of T_c stay within a factor of about two of their microscopic values, while the others fall by up to about six decades, in three groups whose decay is consistent with b^(2y−d) per step for y = 0, −2 and −4 | Machta, Chachra, Transtrum and Sethna (2013), LIT-1299, Fig. 3, read in NOTE-1018. One lattice size, one temperature, at most six steps of b = √2 (so b^n ≤ 8), no error bars, and no fitted rates. The groups and their rates are bands the authors drew. The value y = 0 is not an operator of the 2D Ising model: it is the rate at which any direction without singular support loses information as sites are discarded. The caption’s rate 2^(−d−y) disagrees with the bands and with the supplement’s b^(2y−d). | Proposed |
| THEORY-778 | In the Random Hierarchy Model with v symbols per level, m rules per symbol and s-tuples, the covariance between two tokens whose lowest common ancestor is ℓ levels up has zero mean over grammars and root-mean-square size about ((1 − m/v^(s−1))/(v³ m^(2ℓ−1)))^(1/2), falling by a factor m per level, while its estimate from P sequences carries noise of about (v²P)^(−1/2), so the two meet at P_ℓ ≈ v m^(2ℓ−1)/(1 − m/v^(s−1)); all to leading order in large v and m | Cagnetta and Wyart (2024), LIT-883, App. D–F, read in NOTE-687; re-derived to leading order by the promotion audit and checked against exact covariances of sampled grammars. A statement about the statistics of the generative model only: it says nothing about what a trained network learns, or when, and nothing about natural language. | Active |
| THEORY-779 | In Kunin et al.’s underdamped Langevin model of SGD with momentum on linear regression, with gradient-noise covariance σ²H independent of the parameters, the stationary state is Gaussian with parameter covariance ησ²H(H + λI)⁻¹/(2S(1 − β)) and velocity covariance σ²H/(S(1 − β²)): for small weight decay it spreads equally along every nonzero Hessian direction and not along the null space, each Hessian eigenmode is a damped oscillator with damping ratio (1 − β)/√(2η(1 + β)(ρ + λ)), and the expected squared step is η²σ² tr(H)/(S(1 − β²)) | Kunin et al. (2021), LIT-1011, §§4–6 and App. G, read in NOTE-711; the stationary moments re-derived by the promotion audit. An exact result for a model: Σ ∝ H constant and a quadratic loss are assumptions, and nothing here says a deep network meets them. The probability current is nonzero but reversible: under the model’s assumptions the stationary process is time-reversible once velocities are flipped, so it is “broken detailed balance” only in the paper’s sense, a nonzero current. | Active |
| THEORY-780 | Transcriptional regulation alone can give a bacterium’s gene expression a memory: in E. coli, a transient knockdown or overexpression of one regulator, with the environment held fixed, can leave other genes in a different self-maintaining expression state after it is released, as Zhao, Wytock, Reynolds and Motter predict from a Boolean-network model of its regulatory core | Zhao, Wytock, Reynolds and Motter (2024), LIT-854, read in full in NOTE-655. Their abstract and discussion carry the model result to cells: one genotype may hold several heritable expression states without epigenetic marks, and history picks among them. They predict that a transient crp knockdown leaves zraR, melR or rhaRS changed (NOTE-655, C8, untested). THEORY-178 is the model result this rests on. No such perturbation has been done in cells (QUESTION-172). | Proposed |
| THEORY-781 | Strong gradient noise in SGD, like weight decay above a threshold, makes the subspace fixed by a mirror symmetry of a network’s loss attracting even where it is a saddle, so that networks trained with SGD at large learning rates or small batches reach sparse, low-rank and identical-neuron solutions, as Ziyin proposes | Ziyin (2024), LIT-1014, read in NOTE-716. Beyond the exact half that THEORY-213 holds, the paper argues by a Lyapunov-exponent analysis that strong SGD noise makes a mirror’s subspace attracting even at a strict saddle, and reads sparsity, low rank and identical neurons in trained networks as its result. That analysis rests on a second-order, diagonal- Hessian approximation, and the network evidence is a ResNet18’s correlation blocks. The test is QUESTION-206. | Proposed |
| THEORY-782 | In networks that learn addition from summed embeddings, the critical training fraction of grokking is the fraction at which the training set’s same-answer pairs come to fix the generalising representation up to translation and scale, at every group size, as Liu, Kitouni, Nolte, Michaud, Tegmark and Williams propose | Liu, Kitouni, Nolte, Michaud, Tegmark and Williams (2022), LIT-858, read in NOTE-662, with Power et al.’s critical fraction (LIT-341). The paper presents the critical training fraction as where the training set’s equations fix the embedding. THEORY-181 holds the theorem for the ideal model and the match at the one size measured, p = 10 with 1D embeddings. Held to addition: for S₃ the networks generalise beyond this mechanism. The multi-size test is QUESTION-199. | Proposed |
| THEORY-783 v2 | In neural-network training, sign-descent-like optimizers such as Adam make independent skills of unequal frequency compete for coordinate signs, so that they are learned one after another where gradient descent would learn them together; this is one source of sequential skill onset, beside dependence between skills, as Liu, Liu, Michaud, Gore and Tegmark propose | Liu, Liu, Michaud, Gore and Tegmark (2025), LIT-951, read in NOTE-794. The paper explains the Domino effect, skills starting as others finish, by a coordinate-wise optimizer’s competition for update signs. THEORY-253 holds the simulation in their Geometry model and the rotated quadratic. The paper also shows dependent skills starting after their prerequisites (C5), so the optimizer is one source of sequential onset, not the only one. The test in a trained network is QUESTION-193. | Proposed |
| THEORY-784 | Language models trained on limited data show a test loss falling as P^(−γ/(2β)) because P training tokens resolve token correlations only out to a horizon growing as P^(1/(2β)), so that more data mainly lengthens the context a model can use, when the model learns within that horizon faster than it grows, as Cagnetta, Raventós, Ganguli and Wyart propose | Cagnetta, Raventós, Ganguli and Wyart (2026), LIT-888, read in NOTE-689, building on Cagnetta and Wyart’s effective context window (LIT-883). The paper presents the horizon as the reason the data-limited exponent is γ/(2β). THEORY-204 holds what it showed: the derivation under assumed scaling forms, and the measured overlap on TinyStories and WikiText-103 up to about 10^8 tokens. Whether the horizon is why is the test QUESTION-233 asks. | Proposed |
| THEORY-785 | Listeners interpret an utterance by inverting a model of a speaker who chooses among alternatives by informativeness, so what a fixed form conveys depends on what else the speaker could have said, as the rational speech act account of Frank, Goodman and coauthors proposes | Frank and Goodman (2012), LIT-821, and Goodman and Frank’s review (2016), LIT-816, present listener inference as the inversion of an informative speaker, the rational speech act account. The record holds as shown, in THEORY-172, the fits of that model to mean bets in one-shot reference games and Bergen, Goodman and Levy’s signalling-game result. This is the mechanism the fits were offered for, filed under ADR-047 v4 when the narrowing dropped it. | Proposed |
| THEORY-786 | Deep networks learn hierarchically generated data from a number of examples set by when the correlations between input patches and the class rise above sampling noise, so detecting those correlations is how they learn the grammar, as Cagnetta and coauthors propose | Cagnetta, Petrini, Tomasini, Favero and Wyart (2023), LIT-877, propose that deep networks learn compositional data by detecting the correlations between input patches and the class, and that the sample complexity is where those correlations emerge from sampling noise. The record holds as shown, in THEORY-195, the measured law and the synonym-invariance it coincides with. This is the mechanism, filed under ADR-047 v4 when the narrowing dropped it. | Proposed |
| THEORY-787 v2 | A system’s causal structure can be most effective at a macro scale, so that causation emerges at a coarse-grained level and the macro description is the one at which the system’s causes are found, as Hoel, Albantakis and Tononi propose from effective information | Hoel, Albantakis and Tononi (2013), LIT-1038, argue that macro can beat micro: the scale at which effective information peaks is where a system’s causal structure is, so causation can emerge at a macro level. The record holds as shown, in THEORY-222, only the arithmetic: under uniform interventions imposed separately at each level, a macro description can have more effective information. This is the causal thesis, filed under ADR-047 v4 when the narrowing dropped it. | Rejected — Rejected on 2026-10-30, at the owner’s direction, by its own refutation condition: the macro advantage disappears whenever the same intervention distribution over micro states is used at both levels. THEORY-1167 proves this for a coarse-graining of one transition, by data processing, and Comolatti and Hoel concede it (LIT-1843). The independent interventionist test the promote_when asks for, causal feature learning (LIT-1833), can confirm that a macro is proportionate but never that it beats the micro (THEORY-1169). What the record holds instead is CLAIM-497, by ARG-041. Hoel’s temporal and spatio-temporal macros, which the bound does not reach, are QUESTION-335. The arithmetic it rested on, THEORY-222, stands. |
| THEORY-788 | Training a deep classifier past zero training error generally collapses its last-layer features onto their class means, drives the centred means toward a simplex equiangular tight frame aligned with the classifier, and makes the decision nearest class mean, as Papyan, Han and Donoho propose from their runs | Papyan, Han and Donoho (2020), LIT-618, title their paper on the “prevalence” of neural collapse and present it as a pervasive outcome of the terminal phase of training. The record holds as shown, in THEORY-083, only what their runs measured: three architectures with cross-entropy on seven balanced datasets without augmentation. This is the general law, filed under ADR-047 v4 when the narrowing dropped it. | Proposed |
| THEORY-789 | The block coarse-graining that maximizes mutual information with the system beyond a buffer picks out the renormalization-group-relevant variables in general, so those variables can be found from samples by information alone, without being known beforehand, as Koch-Janusz and Ringel propose | Koch-Janusz and Ringel (2017), LIT-873, propose that their mutual-information criterion finds a system’s relevant degrees of freedom with no prior knowledge of them. What the record holds as shown, THEORY-194, is that it recovered variables renormalization already uses, on 2D models whose answer was known. This is the general thesis that result was offered for, filed under ADR-047 v4 when the narrowing dropped it. | Proposed |
| THEORY-790 | In deep networks trained by SGD on real data, minibatch noise drives parameter groups related by a rescaling symmetry toward the point where their gradient noise balances, at a rate set by learning rate over batch size, so that at stationarity they sit neither where gradient flow would leave them nor spread out as under isotropic noise, as Ziyin, Li and Ueda propose | Ziyin, Li & Ueda, LIT-1012, read in NOTE-714, with the Itô term from LIT-1013. The law of balance is proved in the SDE model of SGD, and that part is the Active THEORY-211. The authors present the law as general to networks with rescaling symmetry, but test it only on small synthetic networks. This THEORY holds the general claim, for deep networks on real data, which no measurement in the record yet supports. | Proposed |
| THEORY-791 | The colour-naming systems of the world’s languages lie near the information-bottleneck bound for compressing perceptual meanings into words, and differences in one trade-off parameter place each language along it, as Zaslavsky, Kemp, Regier and Tishby propose | Zaslavsky, Kemp, Regier & Tishby (2018), LIT-810, read in NOTE-631, using the bound of LIT-338. Their fit covers the World Color Survey languages and English, with the need distribution over meanings estimated from the same naming data, and that measured part is the Active THEORY-163. The authors present the result as a property of the world’s languages. This THEORY holds that general claim. | Proposed |
| THEORY-792 | In a deep linear network trained by gradient descent from generic initial weights, not only from decoupled ones, depth slows learning through the initial end-to-end strength of each mode, so that random orthogonal weights, whose product is an isometry, learn in a number of iterations that stays bounded as depth grows, as Saxe, McClelland and Ganguli argue from simulation | Saxe, McClelland and Ganguli (2014), LIT-864, read in NOTE-667. The exact depth law is proved only from decoupled, balanced starts, and that part is the Active THEORY-187. Beyond it, the paper argues from MNIST runs and random-matrix simulations that random orthogonal layers are such a start in effect, because their product is an isometry, while scaled Gaussian layers are not. This THEORY holds that wider claim, which is argued and simulated and not derived. | Proposed |
| THEORY-793 | Gradient flow on a symmetrized Barlow Twins loss with a linear or fixed-kernel model, from generic small initialization and not only from initialization aligned with the eigenvectors, learns the top eigenvectors of the pairs’ symmetrized cross-correlation one at a time in order of eigenvalue and ends at a top spectral solution, as Simon and coauthors derive informally | Simon et al. (2023), LIT-242, read in NOTE-741. The stepwise dynamics, the minimum-norm end point and the kernel-PCA form are proved from aligned initialization, and that part is the Active THEORY-229. Generic small initialization rests on the paper’s Result 4.6, which its authors style a result and derive informally in App. C, with numerical checks at d = 3. This THEORY holds that generic case. | Proposed |
| THEORY-794 | In vision models, compositional generalization to unseen combinations of concepts is driven by the diversity of the combinations seen in training rather than by data volume, and arrives with representations that are linearly factored by concept, as Uselis, Dittadi and Oh propose | Uselis, Dittadi & Oh (2025), LIT-667, read in NOTE-525. Their title and abstract present diversity of combinations, not data volume, as what drives compositional generalization in vision models. Their evidence is ResNet-50s trained from scratch on two-concept grids, with checkpoints chosen on the unseen pairs, and that measured part, with the factorization theorem, is the Active THEORY-117. This THEORY holds the general causal claim. | Proposed |
| THEORY-795 | On a contested shared canvas, the artworks that last are those whose coalitions keep repairing them under continual overwriting, not those left unattacked, as Wu and Silva propose from the 2017 r/place lifecycles | Wu & Silva (2024; v3 2026), LIT-1032, read in NOTE-724, claim C6 (weak). The persistence thesis drawn from ten illustrated lifecycles, filed apart from what the 2017 log measured (THEORY-216) under ADR-047 v4. It is the population form of what CLAIM-280 needs. | Proposed |
| THEORY-796 | Question-order effects in surveys generally leave the probability of giving the same answer to both questions unchanged, the QQ equality that a projection model of judgment predicts, as Wang, Solloway, Shiffrin and Busemeyer propose | Wang, Solloway, Shiffrin & Busemeyer (2014), LIT-795, after Wang & Busemeyer (2013), LIT-834. The general law the PNAS paper proposes, filed apart from what its 66 Pew surveys and 72 studies measured (THEORY-166) under ADR-047 v4. The equality is a symmetry of Lüders projectors and a classical model with order events can meet it, so the law does not by itself favour quantum probability. | Proposed |
| THEORY-797 | Deep classifiers trained with MSE loss stay near the least-squares classifier for their own features and move along the central path by the dynamics of continually renormalized gradient flow, whose equal-rate growth of the whitened class-separation singular values is how they reach neural collapse, as Han, Papyan and Donoho propose | Han, Papyan & Donoho (2021; ICLR 2022), LIT-974, read in NOTE-783. The paper’s proposed explanation of neural collapse under MSE in real networks, filed apart from its measured central-path proximity and its derivation in a renormalized model (THEORY-278) under ADR-047 v4. Renormalization is imposed, not measured, and every experiment used weight decay, which the derivation excludes. | Proposed |
| THEORY-798 | Independently trained neural encoders of the same data learn latent spaces that differ mainly by an angle-preserving map, a rotation or reflection times a rescaling, so their cosine similarities to shared anchor samples agree across seeds, architectures and languages, as Moschella et al. propose | Moschella, Maiorca, Fumero, Norelli, Locatello & Rodolà (2022; ICLR 2023), LIT-849, read in NOTE-652. The hypothesis behind relative representations, filed apart from what their experiments measured (THEORY-175) under ADR-047 v4. The source assumes it and tests it only through its consequences; it never fits a map between two spaces. | Proposed |
| THEORY-799 | Under geometric coarse-graining of the S¹ hidden-metric network model the average degree flows as r^ν, with ν = 2/(γ − 1) − 1 when the degree exponent γ sets it and 2/β − 1 when β does, so the coarse-grained networks run toward a complete graph for γ < 3 or β < 2 and toward a ring otherwise | The degree flow that THEORY-190’s title carried before the promotion audit (batch 048) narrowed it to the asymptotic closure of the S¹ connection law. García-Pérez, Boguñá and Serrano (2017), LIT-869, derive it to first order by treating the coarse-grained graph as an S¹ model at every separation. The record’s exact computation shows that treatment fails between nearby supernodes, so the flow is unproved. Filed under ADR-047 v4. | Proposed |
| THEORY-800 | A network of N threshold units with symmetric Hebbian couplings stores random patterns as attractors up to a load proportional to N, about 0.15N for all large N, past which recall fails for every pattern at once, and a provision for forgetting old memories, such as couplings that saturate, keeps the most recent ones retrievable however many are added | The large-N and forgetting clauses that THEORY-272’s title carried before the promotion audit (batch 051) narrowed it to Hopfield’s simulations at N = 30 and 100. Hopfield (1982), LIT-918, expects the 0.15N figure “for all large N” from a crosstalk estimate, and states in words that overload makes every memory irretrievable unless old ones are forgotten, with saturating couplings as the mechanism. Filed under ADR-047 v4. | Proposed |
| THEORY-801 v2 | Agents are the systems that would adapt their policy were their actions to affect the world differently, so the agent is wherever that adaptation is: a thermostat is not an agent while it together with its design process is, an RL training process is while its learnt policy generally is not, and humans are | The definition and verdicts THEORY-527’s title carried before the promotion audit (batch 055) narrowed it to the recovery theorem. Kenton, Kumar, Farquhar, Richens, MacDermott and Everitt (2022), LIT-909, propose the definition and argue the verdicts from it in §1 and §4; that it “reliably classifies humans as agents” is asserted. The verdicts are relative to the variables chosen, which the paper states. Filed under ADR-047 v4. | Proposed |
| THEORY-802 v2 | In trained networks as in constructed ones, interchange interventions on a fixed set of variables can be satisfied equally by alignments related by a change of basis, so which internal direction mediates a high-level variable is fixed only relative to a chosen decomposition into units, and complex models will generally have several distinct, fully correct abstractions | The general reading that THEORY-243 held before the promotion audit narrowed it to the three-unit network it proves (batch 062). Wu et al. (2024), LIT-961, conjecture that complex models have “multiple distinct fully correct abstractions” and that the causal-abstraction framework cannot settle structural equivalence; Makelov et al. (2023), LIT-968, §8, grant that crossing component boundaries makes “illusory” tenuous, and answer by privileging components. Filed under ADR-047 v4 so the wide form stays a thesis evidence can confirm or reject. Its only support is the constructed tie. | Proposed |
| THEORY-803 | Real complex networks embedded in the hyperbolic plane are self-similar under geometric renormalization, their coarse-grained layers keeping the degree distribution, clustering and degree–degree correlations of the original, and this self-similarity is evidence that a hidden metric space underlies them | The empirical claim THEORY-190 set aside when the promotion audit (batch 048) narrowed it to the model. García-Pérez, Boguñá and Serrano (2017), LIT-869, find six embedded real networks self-similar under the renormalization and call this new evidence of hidden metric spaces. The collapse was judged by eye over two to five layers with no null ordering of the circle. Filed under ADR-047 v4. | Proposed |
| THEORY-804 | Ince’s common change in surprisal is a correct measure of the redundancy among any number of sources, and the negative partial-information atoms it gives are local misinformation and mechanistic redundancy, not defects of the measure | The thesis THEORY-714’s title carried before the promotion audit (batch 056) corrected and narrowed it to what I_ccs is and which properties it has. Ince (2017), LIT-1201, proposes I_ccs as the redundancy measure and reads its negative atoms as misinformation and mechanistic redundancy. Filed under ADR-047 v4. The re-derivation found that I_ccs fails subset equality, the property Ince argues licenses the lattice, which counts against the thesis without settling it. | Proposed |
| THEORY-805 | Volume-maximizing joint-embedding objectives as a class, VICReg and SimCLR as well as MSN and SwAV, carry a prior toward equal-sized clusters, and that prior costs them semantic transfer when the pretraining data are class-imbalanced, including on naturally long-tailed data | The general reading that THEORY-306 held before the promotion audit narrowed it to the explicit priors of MSN and SwAV and to one experiment with two to eight classes per batch (batch 033). Assran et al. (2022), LIT-231, read in NOTE-850, argue the prior for the whole class, VICReg through an informal reduction to K-means and SimCLR through a cited equivalence, and read it as the cause of the degradation reported on real long-tailed data. Filed under ADR-047 v4 so the wide form stays a thesis evidence can confirm or reject. | Proposed |
| THEORY-806 | Translation without parallel data, as of an unknown animal communication system into a human language, is learnable from a plausibility prior over the target language alone, with error falling as the common ground between the languages grows and as the source language grows richer | The general reading that THEORY-270 held before the promotion audit narrowed it to the common-nonsense model its bound is proved in (batch 044). Goldwasser, Gruber, Kalai and Paradise (NeurIPS 2023), LIT-941, read in NOTE-804, motivate their framework by translating animal communication and state its lesson for translation in general, while saying their stylised models are not intended to capture natural language. Filed under ADR-047 v4 so the wide form stays a thesis evidence can confirm or reject. | Proposed |
| THEORY-807 | The guppy-type overextension in Hampton’s membership data arises because a combined concept is in part a new, emergent concept and not only a logical combination of its parts, so human concept combination runs in two superposed layers, one classical and logical and one quantum and conceptual | Aerts’s reading, which THEORY-255’s title carried before the promotion audit narrowed it (batch 018) to the impossibility Theorem 9 proves. Aerts (2009), LIT-934, read in NOTE-808, fits the ∆-type deviations with one emergent subspace per pair and reads thought as two superposed layers. The narrowing was right that the theorem does not force an emergent concept, only dropping the meet or the monotone weight; this entry is the emergence reading as Aerts’s thesis. Filed under ADR-047 v4 so the wide form stays a thesis evidence can confirm or reject. | Proposed |
| THEORY-808 | Transformers trained by next-token prediction on sequence processes whose latent dynamics factor as a tensor product learn to represent the belief state in approximately orthogonal per-factor subspaces of about the factored dimension rather than the joint one, and reach that factored representation first even when noise makes it lossy | The general reading that THEORY-256 held before the promotion audit narrowed it to the five Mess3 and Bloch Walk factors and the 4-layer GPT-2-style models tested (batch 019). Shai et al. (2026), LIT-986, read in NOTE-758, present next-token training (the paper is titled “Transformers learn factored representations”) as yielding factored, orthogonal belief representations; NOTE-758’s claims C2 to C4 are each shown on one family of synthetic processes. Filed under ADR-047 v4 so the wide form stays a thesis evidence can confirm or reject. It does not include the paper’s inference that the preference is architectural (C5), which App. D.4 leaves open, or the claim that the factored form persists at convergence under strong noise, which Fig. 12 contradicts. | Proposed |
| THEORY-809 | Language models trained by gradient descent on a mixture of random facts and other data reach the capacity-optimal allocation, so the model size and the mixing ratio at which they begin to learn the facts are those of an optimal capacity-bounded learner | The link that THEORY-293’s title asserted before the promotion audit narrowed it (batch 036) to the optimal learner’s theorem and the observation of a threshold in Pythia models. Gu, Lyu, Li and Zhang (2025), LIT-984, read in NOTE-796, explain the trained models’ thresholds by the optimal learner’s. The one quantitative check, a size exponent of 1.152 against a predicted 1.283, is recorded against it. Filed under ADR-047 v4 so the wide form stays a thesis evidence can confirm or reject. | Proposed |
| THEORY-810 | Prediction-market prices keep much of an arbitrary price shock that no trader’s information supports for weeks, rather than correcting it within a short transition phase | The general reading that THEORY-267 held before the promotion audit narrowed it to the 817 Manifold play-money markets measured. Rasooly and Rozzi (2025), LIT-958, read in NOTE-778, set the result against the received view (Wolfers and Zitzewitz, 2004) that manipulation matters only briefly, and offer it as a finding about prediction markets. Their evidence is one platform, at play-money stakes. Filed under ADR-047 v4 so the wide form stays a thesis evidence can confirm or reject. | Proposed |
| THEORY-811 | With a kernel normalised to unit diagonal, the kernel quantum relative entropy of two distributions is within O(σ²) of their Kullback–Leibler divergence as the bandwidth σ shrinks, for translation-invariant kernels on the torus generally and for kernels on other compact groups | The general reading that THEORY-313 held before the promotion audit narrowed it to the one kernel family on the torus that the rate is shown for. Bach (2022), LIT-255, read in NOTE-837, asserts that other translation-invariant kernels and kernels on compact groups behave alike, and sketches a leverage-score argument without completing it. Filed under ADR-047 v4 so the wide form stays a thesis evidence can confirm or reject. | Proposed |
| THEORY-812 | As dimension grows with the undersampling and sparsity ratios fixed, the ℓ₁ phase transition for recovering sparse vectors from random measurements sits at the same curve for a broad class of random-matrix ensembles, those with a kind of orthogonality or weak independence, as for Gaussian matrices, while differing at finite size | The general reading that THEORY-391 held before the promotion audit narrowed it to what 2,948,000 optimizations at three problem sizes showed. Donoho and Tanner (2009), LIT-1160, read in NOTE-933, state it as the hypothesis of “weak universality” and pose the class of ensembles it holds for as an open problem. Nothing about non-Gaussian ensembles is proved. Filed under ADR-047 v4 so the wide form stays a thesis evidence can confirm or reject. | Proposed |
| THEORY-813 | Training a wide network in the lazy, kernel regime does not make its features more collapsed than at initialization, so neural collapse, where it occurs, is something only feature learning produces | The general reading that THEORY-294 held before the promotion audit narrowed it to the one-dimensional, zero-bias, two-class case it proves. Kothapalli and Tirer (2024), LIT-985, read in NOTE-774, draw it as their conclusion: the lazy regime does not collapse anything, so the data-dependence of collapse has to come from a kernel that moves with the data. Beyond the solved case their support is simulation on two-class Gaussian data, where the NTK comes out less collapsed than the NNGP. Filed under ADR-047 v4 so the wide form stays a thesis evidence can confirm or reject. | Proposed |
| THEORY-814 | In scientific communities that settle on a consensus model by sound model comparisons, high reproducibility of results is not evidence that the consensus is true, because which alternatives get proposed can hold a false consensus whose results reproduce almost perfectly | The general reading that THEORY-295 held before the promotion audit narrowed it to the memoryless consensus model it proves. Devezer, Nardin, Baumgaertner and Buzbas (2019), LIT-988, read in NOTE-792, present the decoupling of reproducibility from truth as a lesson for science, not only for their model. Their model has no beliefs, no learning and no memory in the consensus. Filed under ADR-047 v4 so the wide form stays a thesis evidence can confirm or reject. | Proposed |
| THEORY-815 | Layering a navigable small-world graph on nested random subsets of the data, with links separated by length scale and each layer’s degree capped, makes greedy nearest-neighbour search cost grow logarithmically with the number of items on data of low intrinsic dimension, where the single-layer graph’s cost grows polylogarithmically | Malkov and Yashunin (2020), LIT-1098, read in NOTE-916, argue that HNSW’s hierarchy is what makes greedy search logarithmic: constant cost per layer over O(log N) layers, against the polylogarithmic cost of their earlier flat graph. The record holds as measured, in THEORY-365, logarithmic-or-better cost on uniform data in 8 dimensions and a saturating beam width in 4. The bound is derived only for exact Delaunay layers, which HNSW does not build, and on 200 million SIFT vectors the paper’s own scaling departs from a logarithm, so the thesis is stated for low intrinsic dimension. | Proposed |
| THEORY-816 | Learners inferring what a novel word means from its use reason about a speaker who chose the word to be informative about the referent, so the size principle in word learning is a consequence of that inference and not a separate rule of generalisation | Frank, Goodman, Lai and Tenenbaum (2009), LIT-824, read in NOTE-627, derive the size principle from an informative speaker and present the word learner as inverting that speaker. The record holds as shown, in THEORY-472, the derivation and one experiment in which mean bets matched the inversion; in those displays an informative-speaker learner and a plain size-principle learner coincide, so whether learners reason about the speaker is open. THEORY-785 is the same inversion for listeners in reference games. | Proposed |
| THEORY-817 | Once an agent’s actions affect the percepts it receives, maximal prediction of those percepts is generally not what thermodynamic efficiency requires: in percept-action loops with feedback, maximally predictive agents generally extract less work than the most efficient agent | Fiderer et al. (2025), LIT-041, read in NOTE-032, prove that without feedback the work-efficient agents are exactly the maximally predictive ones that randomise and forget their actions, and that with feedback one binary memoryless channel separates predictive, max-entropy-action and efficient agents; from that they assert that with feedback maximally predictive agents are generally inefficient. The record holds as proved, in THEORY-026, only the one channel. It does not say that efficiency under feedback is a trade-off between prediction and forgetting: in the proved example the efficient agent is memoryless. | Proposed |
| THEORY-818 v2 | In two-scale Lorenz 96 without time-scale separation (ε = 0.5, K = 18, J = 20, F = 10), a discrete-time closure for each resolved variable that fits the one-step discrepancy of a fourth-order Runge–Kutta step as a NARMAX series, with one autoregressive lag, at most two lags of the resolved variable and at most one moving-average term, reproduces the mean, spread, distribution, autocorrelation and neighbour cross-correlation of x₁ (Kolmogorov–Smirnov distance 0.005) and, with observations every 0.05, extends the 20-member ensemble forecast lead time at anomaly correlation 0.6 from about 2 to about 4 time units over a polynomial-plus-AR(1) closure; the model structure was chosen by trial and error, differs between the two observation spacings, and carries no error bound | Chorin and Lu (2015), LIT-1304, read in NOTE-1028. A data-driven closure with one or two steps of discrete memory, plus one moving-average innovation, is enough on this test to reproduce the resolved statistics and to double forecast skill against a memoryless-in-x closure. It is the record’s first evidence that a short discrete memory suffices in a chaotic system with no scale gap. It is one system, the structure was tuned, and there is no bound, so it does not give the controlled prediction error QUESTION-222 asks for. | Active |
| THEORY-819 | For an invertible map with an invariant measure, projecting onto the closed span of the whole past of chosen functions of the resolved variables (a Wiener projection) turns the exact discrete Mori–Zwanzig equation into one with no memory term: the next resolved value is a causal linear filter of those past functions plus a residual orthogonal to all of them, so the memory is carried by the coarse variable’s own history; a finite NARMAX form follows only by a rational approximation of the filter, uncontrolled in general but exact for a scalar coarse variable of a stable linear Gaussian VAR(1) | Lin and Lu (2021), LIT-1307, read in NOTE-1029. Mori–Zwanzig’s memory is what a projection onto the present leaves out; a projection onto the whole past absorbs it, leaving the causal Wiener filter on the coarse variable’s own history and a residual orthogonal to all of that history. Second-order (linear-span) projections, invertible dynamics and stationarity only. It gives no finite augmentation with a bounded error in general: the NARMAX step is the paper’s uncontrolled approximation, exact only in the linear Gaussian class shown here. | Active |
| THEORY-820 v2 | For a stationary discrete-valued process X and any coarse-graining Z of its past, informational closure at every horizon is the same condition as zero one-step transfer entropy from the micro past, Barnett and Seth’s dynamical independence, and as causal closure, Z’s ε-machine coinciding with its υ-machine; for a coarse-graining of the present state it also makes Z’s causal states a coarse-graining of X’s, which does not imply closure, and the closed coarse-grainings are not closed under common refinement | Rosas et al. (arXiv 2024), LIT-1306, read in NOTE-1030, with Barnett and Seth’s definition (LIT-979). For discrete stationary processes, the information-theoretic criterion of emergent closure (dynamical independence), the interventionist one (the macro’s own causal states are all the micro distinctions that matter for it) and, for maps of the present state, a computational one are nested as stated. The first two are one condition. It says nothing about approximate closure. It does not make closure a mark of unity. “Causal” is only in the Granger sense unless X is fully observed. | Active |
| THEORY-821 | For every α < 1/15 there are weak solutions of the 3D incompressible Euler equations on the periodic box, Hölder-continuous of exponent α in space and time, that satisfy the local energy inequality; in the construction their dissipation measure is a nonnegative function of time alone, equal at each time to the rate at which the total energy falls, zero while the local energy equality holds and positive on all of space during a short final interval in which the solution’s energy is drained to zero; uncountably many such solutions share one initial datum and one dissipation measure; for them the local coarse-grained energy flux into vanishing scales converges to that measure, so the transfer is one-way at every place and time in the limit and spread uniformly over the box, with its timing chosen by the construction, not forced by the equations | Isett (2017; ARMA 2022), LIT-1305, skimmed in NOTE-1027: the first continuous, indeed C^α with α < 1/15, weak Euler solutions satisfying the local energy inequality with nonzero dissipation, and a Cantor family of them sharing one initial datum and one dissipation measure. In the construction the dissipation measure is a function of time alone, so in the limit of vanishing scale the energy flux runs one way at every place, as in THEORY-772, but in a Hölder class and spread uniformly over the torus rather than set in pipes. It is switched on only while the constructor drains the solution’s energy to zero at the end of its life. Where, when and how fast the energy goes are inputs; the exponent is far from 1/3; nothing ties these solutions to Navier–Stokes. | Proposed |
| THEORY-822 | For a Markov chain and a partition of its states, strong lumpability, every state of a block sending the same probability into each block, is the column-equitability of the master-equation operator and makes the block label informationally closed; when the chain is irreducible, an informationally closed label that is itself Markov is strongly lumpable, with no aperiodicity needed; weak lumpability gives a Markov label that need not be closed; and the same holds on the causal-state chain of any stationary process | Rosas et al. (arXiv 2024), LIT-1306, read in NOTE-1030, on Kemeny–Snell lumpability, joined to Shpak et al.’s column-equitable partitions (LIT-1242, THEORY-755). Exact closure of a block label in a Markov chain is a condition on transition rows, a symmetry, and not weak coupling. The converse needs the label to be Markov: a closed label can have memory. Exact results only, with no bound for nearly lumpable partitions. | Active |
| THEORY-823 | Tetris players rotate pieces more often than planning a placement and then executing it would require, rotate them early and check the column more the higher the drop, because these moves are epistemic actions: physical action that stands in for mental computation at the moment of use | Kirsh and Maglio (1994), LIT-1054, read in full in NOTE-878, with Kirsh (1995), LIT-1076, read in NOTE-871, argue that the extra, early and checking moves of Tetris players are epistemic actions: physical moves whose primary function is to cut the space, time or unreliability of the player’s own computation. The record holds as shown, in THEORY-360, only the early-rotation timing and the drop-length difference after the wall check. Over-rotation and the rise of the check with drop height rest on figures without printed numbers, and the saving is argued from a three-player pilot, not measured. Filed under ADR-047 v4 when the narrowing dropped it. | Proposed |
| THEORY-824 | Economics working papers increasingly back their claims with design-based identification: in NBER and CEPR working papers the share of claims supported by difference-in-differences, instrumental variables, an RCT, regression discontinuity or synthetic control rose about fourfold from 1990 to 2020 | Garg and Fetzer (2024; arXiv v2 2026), LIT-079, read in full in NOTE-083, read the rise in their extraction’s design-backed share as a change in economics: “economic papers have increasingly incorporated causal inference methods to substantiate their claims over the past three decades”. The record holds as shown, in THEORY-674, only the extraction’s series, whose edges were never checked against human labels and whose per-decade slope nearly vanishes with method-mix and graph-volume controls. This is the paper’s reading, filed under ADR-047 v4 when the narrowing dropped it. | Proposed |
| THEORY-825 | Hyperbolic graph embedding models trained on task losses that never mention the hierarchy do not place a tree’s root nearest the origin, and their distance from the origin orders hierarchical levels only partly | Yang, Zhou, Ying, Chen & King (2023), LIT-871, read in NOTE-669, assert for hyperbolic graph models in general what they measured for HGCN on two synthetic trees: the root is not innermost and radius reads level only partly. The general form was the lead clause of THEORY-421 until that account was narrowed to the measurement on 2026-10-20 (ADR-047 v4); it is filed here so that it stays a thesis evidence can confirm or reject. | Proposed |
| THEORY-826 | In work groups, a member’s displayed mood spreads to the others, and pleasant emotional contagion improves the group’s cooperation and reduces its conflict | Barsade (2002), LIT-706, read in NOTE-551, presents emotional contagion as a general phenomenon of work groups and states its effect on group process causally: “this contagion improved cooperation, decreased conflict”. The record holds as shown, in THEORY-123, only what her two studies measured: ad hoc student groups, one actor as the source, and a process link that is a correlation with measured contagion. This is her wider claim, filed under ADR-047 v4 when the narrowing dropped it. | Proposed |
| THEORY-827 | The rubber hand illusion is a perceptual illusion driven by multisensory integration: the difference in reports between synchronous and asynchronous brushing is produced by the stimulation, not by participants’ expectations | Ehrsson et al. (2022), LIT-1264, read in NOTE-997, conclude that the rubber hand illusion is a perceptual illusion driven primarily by multisensory mechanisms (NOTE-997, C8), from the synchrony difference’s independence of hypnotisability in Lush et al.’s 353 participants. Lush and Seth’s reply, LIT-1267, shows that uniform but unequal expectations predict the same null. The record holds as shown, in THEORY-766, only the report differences and that the standard controls do not equalise expectations. This is the perceptual reading, filed under ADR-047 v4 when that narrowing set it aside. | Proposed |
| THEORY-828 | Fine-tuning from one pretrained model typically lands near the edge of a task-specific low-loss region in weight space that contains the convex hull of the fine-tuned models, and averaging their weights, as model soups and stochastic weight averaging do, works by moving inward | Gueta, Venezian, Raffel, Slonim, Katz and Choshen (2023), LIT-658, read in NOTE-515, conclude that fine-tuning “typically” yields models on the boundary of a region whose centre is better, and read model soups and SWA as picking points inside it (§§8–9). The record holds as shown, in THEORY-105, only the probe-loss comparisons of hull points with members and the BitFit result, for RoBERTa-base on English classification. This is their geometric thesis, filed under ADR-047 v4 when the narrowing dropped it. | Proposed |
| THEORY-829 | In Hrbacek’s relative analysis, if belief at a context level is credence ultraclose to 1 at that level, the conjunction of any standard number of believed propositions is believed, while for an ultralarge number it can fail: in a fair lottery with an ultralarge number of tickets each ‘this ticket loses’ is believed and their conjunction has probability 0 | Wenmackers (2011), LIT-163, Ch. 3 (Stratified Belief, Def. 1; the Stratified Conjunction Principle, Def. 2, eq. 3.5 and §3.6.3.2), read in full in NOTE-139; re-derived by the promotion audit from finite subadditivity and Hrbacek’s Closure principle. A result inside the framework: it says nothing about whether belief has levels, and any explicit level boundary collapses the model back to a fixed threshold. | Active |
| THEORY-830 | In human visual cortex the content of a sustained seen image is carried by a stable population code that lasts as long as the image, not by a sustained level of activity, and frontoparietal cortex marks only its onset; so a sustained experience rests on sensory representation and its discrete updates on frontoparietal representation | Vishne, Gerber, Knight and Deouell (2023), LIT-644, read in full in NOTE-499, conclude from their intracranial recordings that sustained visual experience may rest on a stable sensory representation, with frontoparietal representation serving discrete updates, and propose a stable “experience subspace”. Their measurement, in ten patients and for images up to 1.5 s, is the Active THEORY-102. This is the general claim that measurement was filed to support, held Proposed until a second method or cohort and a case where percept and input come apart test it. | Proposed |
| THEORY-831 | For a system driven by a protocol fixed in advance, with microscopic reversibility and with forward and reverse processes started uniformly on their macrostates, the log-odds of two outcomes II and III reached from I equal the difference in their log state counts, plus the log-ratio of their reversal probabilities, plus the difference in minus the log mean of e^(−βQ) over the paths reaching each, where Q is the heat released; so when the first two terms are equal the likelier outcome is the one whose paths release more heat on average with less variation | Perunov, Marsland and England (2016), LIT-518, Eq. (8), read in full in NOTE-416 (which checked Eqs. 3–8), building on England’s macrostate relation (2013), LIT-515; re-derived by the promotion audit. An exact identity from microscopic reversibility, under a fixed protocol and uniform starting densities; the paper itself uses near-uniformity. It says nothing about which macrostates a real many-body system can be divided into with the other two terms equal. | Active |
| THEORY-832 | For strict combining functions and m attribute-sorted lists of N objects whose orderings are probabilistically independent, no correct top-k algorithm does essentially better than Fagin’s Algorithm in the worst case with high probability: every one needs on the order of N^((m−1)/m) k^(1/m) accesses | Fagin (1996/1999), LIT-1108, as reported by Fagin, Lotem and Naor (2001), LIT-1115, Sections 1 and 3, read in NOTE-924: “his algorithm is optimal with high probability in the worst case if the aggregation function is strict … and if the orderings in the sorted lists are probabilistically independent.” Strict means the combined grade is 1 exactly when every grade is 1. Not read in the original; not re-derived. | Proposed |
| THEORY-833 | In a 2024 survey of a quota-matched online sample of 2,092 US adults and a convenience sample of 103 antitrust lawyers, the public weighed layoffs, worse product quality and more lobbying well above price reductions in judging whether a merger should be challenged, the consumer welfare standard’s own objective, while support for replacing that standard was 42.6 points lower among the lawyers than among the public, against a partisan gap of 5.9 points | Short, Hill and Brown (2025), LIT-1327, read in NOTE-1051. A pre-registered conjoint and opinion survey. It does not say that the samples represent the US public or the antitrust bar, that the lawyers’ training caused their values, or that the standard is captured: that verdict also needs the paper’s historical argument and is THEORY-859, Proposed. | Active |
| THEORY-834 v2 | A member of a discipline who has been trained into its paradigms yet remains rooted in experience those paradigms omit or distort is better placed than its insiders to perceive those omissions and distortions as anomalies, and better placed than outsiders who share the experience to have them taken up, because insiders share the assumptions that produced the anomalies and outsiders lack the professional authority to press them | Collins (1986), LIT-1312, read in an authorized Portuguese translation in NOTE-1042: the “outsider within”. An argument from the sociology of knowledge and Kuhn, illustrated by anomalies Black feminist sociologists did detect. It does not say that every outsider within sees them, that insiders cannot, or that what the outsider within reports is true; and it offers no comparison of who detects what. | Proposed |
| THEORY-835 | When two firms each hire the best available candidate by a noisy ranking, and the ranking model makes an independent re-ranking worth more to the second mover than its own next choice and makes a weaker first mover better for it, then for every accuracy of the private rankings there is a more accurate shared algorithmic ranking that each firm strictly prefers to use whatever the other does, and with which both firms, and total welfare, do worse than if neither used it | Kleinberg and Raghavan (2021), LIT-1326, read in NOTE-1033. A Braess paradox for screening: the shared algorithm’s accuracy helps whoever chooses first and its correlation hurts whoever chooses second, and at the right accuracy the second effect wins while adoption stays dominant. It holds for the Mallows model always and for some random utility models, and never for Plackett–Luce. It says nothing about shocks, dynamics or market responses. | Active |
| THEORY-836 | Scored between Nicaragua’s regime-owned outlets and its exiled or online opposition outlets, on the prevalence of topics relevant to the regime’s legitimacy and on the tone of sentences mentioning Ortega, the three nominally independent national outlets with web output moved toward the regime pole in agenda over 2018–2022, Canal 14 most and Radio Corporación least, and Canal 14’s tone score fell from about .8 to below .5 by early 2022 while Radio Corporación’s stayed near 1 | Barnehl and Schumacher (2024), LIT-1323, read in NOTE-1047. A measured shift in relative position, outlet by outlet, from a 30-topic structural topic model and an off-the-shelf Spanish sentiment classifier, with no uncertainty reported in the main text. It does not show that the shift was coerced, which the paper’s own definition of capture requires, nor that the opposition pole held still. | Active |
| THEORY-837 | In Besley and Prat’s model of an incumbent who can pay n identical outlets to suppress verifiable bad news, where one outlet’s report informs every voter, each outlet’s price for silence is what it would earn as the only one to break the story, so the media are captured exactly when n·τa < r; under capture voters, though fully rational and not deceived, learn nothing and never remove a bad incumbent | Besley and Prat (2006; read in the 2005 LSE working paper), LIT-1333, read in NOTE-1031. Plurality protects because news is non-rival: silencing the press means silencing every outlet, each at its monopoly price. A static, hard-news model. It says nothing about soft news, partial bribing, or capture that feeds back on the market that permits it, and its cross-country evidence is a raw comparison of means. | Active |
| THEORY-838 | The emphasis the news media give to issues raises the importance their audiences assign those issues, independently of any change in the audiences’ attitudes toward the issues: the media influence what people think about more than what they think | The agenda-setting hypothesis, as McCombs and Shaw (1972), LIT-1335, state it after Cohen and the Langs, read in NOTE-1046. Their evidence is an aggregate correlation in one sample, held as THEORY-842; the direction from media to public is argued there, not identified. The later literature the programme produced is not read here. | Proposed |
| THEORY-839 | A model optimal for the distribution its own deployment induces, a performatively stable point, need not minimize the risk it actually incurs, and the gap is bounded: for a loss that is L_z-Lipschitz in the data and γ-strongly convex in the parameters, and a distribution map that is ε-Lipschitz in Wasserstein-1 distance, every stable point lies within 2L_zε/γ of every performative optimum; in a biased-coin example the stable point is µ/(1 − ε) and the optimum µ/(1 − 2ε), equal only when the prediction has no effect | Perdomo, Zrnic, Mendler-Dünner and Hardt (2020), LIT-1336, read in NOTE-1044. Self-consistency under one’s own influence and the best outcome under that influence are different targets. The bound says they are close when the influence is weak relative to the loss’s curvature. It does not say how to find the optimum, which needs the distribution map away from the deployed model. | Active |
| THEORY-840 | When every log-likelihood a predictive family V can assign lies in [−B, B], the V-information estimated from N samples is within 4R_N(G_V) + 2B√(2 log(1/δ)/N) of the true V-information with probability at least 1 − 2δ, with R_N(G_V) the Rademacher complexity of the family’s log-likelihoods; so usable information relative to a family of small complexity can be estimated in high dimension, and what is estimated is that family’s information, not Shannon’s | Xu, Zhao, Song, Stewart and Ermon (2020), LIT-1309, read in NOTE-1048, Theorem 1. Restricting the predictor class trades the data-processing inequality for estimability. The bound needs bounded log-likelihoods and says nothing about Shannon information, which a restricted family may under- or over-state (THEORY-846). | Active |
| THEORY-841 | Knowledge of the particular circumstances of time and place is held dispersed among many people and cannot be conveyed to a central authority in statistical form, so decisions that depend on it are better taken by those who hold it, and a price system lets them fit their decisions together by conveying the relative scarcities each needs without the causes behind them | Hayek (1945), LIT-1337, read in NOTE-1036. An argument, not a result: the essay gives examples (the tin shortage, the shipper, the arbitrageur) and an analogy to the rates of substitution a single mind uses, and no model of how well prices convey what decisions need. It says nothing about what prices fail to carry, and it does not argue that removing any particular public constraint decentralizes decisions. | Proposed |
| THEORY-842 | Among 100 Chapel Hill voters not yet committed to a candidate in September–October 1968, the aggregate emphasis they gave the campaign’s main issues correlated +.967 with the emphasis of the major news items, and +.979 with that of the minor items, in the nine media serving them; and voters leaning to a candidate agreed more with all the news than with news about their own side in 18 of 24 comparisons | McCombs and Shaw (1972), LIT-1335, read in NOTE-1046. An aggregate correlation between a public’s ranking of issues and the media’s, in one community, one campaign and one sample of 100 undecided voters. It does not show that the media’s emphasis caused the voters’ ranking; the authors say the correlations do not prove agenda-setting. | Active |
| THEORY-843 | Beckers, Eberhardt and Halpern’s approximate abstraction error, the least over surjective context maps of the worst case over allowed interventions and contexts of the high-level distance between the coarse-grained low-level outcome and the high-level outcome, is zero exactly for τ-abstraction; an abstraction followed by an α-approximation of the high-level model is within α, an α-approximation of the low-level model followed by an abstraction only within kα, k the worst-case ratio of high- to low-level distances, and an approximate abstraction need not factor into an exact abstraction and an approximation | Beckers, Eberhardt and Halpern (2020; arXiv 2019), LIT-1310, read in NOTE-1045, on Beckers and Halpern’s τ-abstraction (LIT-1316). The error is relative to a metric the user chooses, takes the worst case over interventions, and minimizes over context maps, so like exact abstraction it is zero for a coarse-graining whose dropped detail the high-level noise can hold. It does not measure the governance deficiency Γ. | Active |
| THEORY-844 | A designer who commits to how players are informed, and may condition on the state and on their prior information but cannot choose their actions, can bring about exactly the Bayes correlated equilibria, the joint distributions of states and actions in which no player told his recommended action wants to deviate, a polytope cut out by linear constraints; with one uninformed receiver who would lose 1 by investing in the bad state and gain x < 1 in the good, the most investment attainable is certain investment in the good state and investment with probability x in the bad | Bergemann and Morris (2019), LIT-1313, read in NOTE-1034, from the accepted manuscript. What control over information alone can achieve, among Bayesian players with a common prior, is a set computable by linear programming, whoever the designer is, and read metaphorically it bounds what any information structure could produce. It assumes commitment, a designer who picks the equilibrium, and Bayesian players; it says nothing about bounded receivers. | Active |
| THEORY-845 | In Weatherall, O’Connor and Bruner’s network model a policy maker’s credence depends on the evidence it has received only through the total excess of successes over failures of the new action, so a propagandist’s effect is the excess of failures it adds; for the same pulls, running single-trial studies and publishing the failures adds at least as large an excess as any other division into studies, which is why biased production does best with the smallest studies | Weatherall, O’Connor and Bruner (2020; arXiv 2018), LIT-1341, read in NOTE-1038. With two symmetric hypotheses, each result’s likelihood ratio depends only on successes minus failures, so the audience’s belief is a monotone function of the cumulative excess; whoever chooses what the audience sees chooses that number. It holds for the paper’s two-point hypothesis space and naive updating, and says nothing about richer hypothesis spaces or audiences that model the selection. | Active |
| THEORY-846 | Information usable by a predictor restricted to a family V can be created by computing on the data, so the data-processing inequality fails for V-information: with Z the exclusive-or of two fair independent bits, linear and one-coordinate families extract nothing about Z from the pair and all of it from their exclusive-or; V-information computed from any function of the source is bounded by the source’s Shannon information when the family’s input-free predictions can match the marginal of the target, and can exceed it otherwise | Xu, Zhao, Song, Stewart and Ermon (2020), LIT-1309, read in NOTE-1048, define V-information and say it “can be created through computation”. The record’s worked case is CLAIM-199’s XOR under the paper’s linear families, and its addition is the ceiling: usable information never exceeds the source’s Shannon information when V can predict the marginal of Y without input, and can exceed it when V cannot. It says nothing about which family a real observer has. | Active |
| THEORY-847 | In a linear structural equation model whose exogenous micro-causes W₁, …, W_n drive effects Z = AW + F, with interventions that set all of W, all of Z or both, averaging each block is an exact transformation onto Ẑ = (an/m)Ŵ + F̂ if and only if every column of A sums to the same a, the column-equitability of the block of A from W to Z; the transformation is exact only for those whole-block interventions | Rubenstein et al. (2017), LIT-1334, read in NOTE-1037, with Beckers and Halpern’s restatement (LIT-1316, Example 3.3). Averages of linear micro-variables form a causally consistent macro model exactly when each micro-cause has the same total effect on the effect block. It says nothing about interventions on single micro-variables, which break exactness, nor about nonlinear or approximate aggregation. | Active |
| THEORY-848 | In an acyclic structural equation model, marginalising a variable that no declared intervention sets is an exact transformation, provided the coarse model’s exogenous noises may be dependent; so exactness does not require the dropped variable to be causally idle, and it can drop a variable that decides how its children respond to an intervention that is declared | Rubenstein et al. (2017), LIT-1334, read in NOTE-1037. Exact transformation asks only that the coarse model reproduce the push-forward of each declared interventional law, so a never-intervened variable can be substituted out and its randomness folded into noise, whatever it does. Applied to the hidden governance bit, the coarse-graining that CLAIM-407 shows to lose the response to h is exact. It does not say that the coarse model keeps any one system’s response. | Active |
| THEORY-849 | For deterministic causal models with a countable set of allowed interventions, a high-level model reproduces the coarse-grained interventional law of a low-level one for every distribution on contexts exactly when some map τ_U on contexts commutes with every allowed intervention, τ(M_L(u, i)) = M_H(τ_U(u), ω(i)); exactness for one distribution is strictly weaker, since a well-chosen distribution lets unrelated models match, and τ-abstraction and strong abstraction are strictly stronger; the context map is only required to exist, so high-level exogenous variables may carry what the coarse state drops | Beckers and Halpern (2019), LIT-1316, read in NOTE-1032, on Rubenstein et al.’s exact transformation (LIT-1334). Uniformity over distributions turns a distributional match into a context-by-context commuting condition. It does not make the coarse endogenous state carry the high-level context, which is what governance-response sufficiency would need. | Active |
| THEORY-850 v2 | In Hungary, 1994–2016, state-owned firms’ advertising, and not private firms’, shifted sharply toward print and online outlets when they became connected to the governing right and away when the 2015 Orbán–Simicska fallout ended a connection, at all five such events studied; and the outlets’ share of articles on corruption scandals moved the opposite way at the three events with content data | Szeidl and Szucs (2021), LIT-1315, read in NOTE-1039. Two-way favors in the reduced form: government-controlled advertising follows connection status where private advertising does not, and corruption coverage moves against it. Hungary under right-wing governments only; left-wing favoritism is not settled, and the reduced form does not say whether content favors were bought or shared. | Active |
| THEORY-851 | In Argentina’s four main national newspapers, April 1998 to December 2007, a newspaper’s monthly front-page coverage of the federal government’s corruption scandals was lower in months when it received more government advertising, within newspaper and month and within each newspaper-president pair (about 0.31 of a front page per standard deviation of advertising in the 2010 working paper); the association held for advertising placed through the presidency’s agency and not for autonomous agencies, and not for scandals of non-political actors | Di Tella and Franceschelli (NBER 2009, revised 2010; AEJ: Applied 2011), LIT-1319, read in NOTE-1040. An association within newspaper and within presidency, specific to discretionary advertising and to the government’s own scandals. It does not establish that advertising caused the reduced coverage, and the published version reports a smaller effect (0.23 of a front page, 18 percent of a standard deviation), which was not checked here. | Active |
| THEORY-852 v2 | Under Szeidl and Szucs’s structural model and its identifying assumptions (an owner’s ideology fixed across episodes; the government’s online advertising budget not driven by the outlets’ slant), both owner ideology and favor exchange drove the Hungarian portal Origo’s reduced coverage of corruption in 2013–2016: favor exchange alone cut it by 29–44%, the new owner’s ideology alone by 63% after 2016, and the two together by 74%, so they are substitutes; and a ban on targeted government advertising would have raised it by 41–79% | Szeidl and Szucs (2021), LIT-1315, read in NOTE-1039. Table IV’s estimates (weight on profit β ≈ 1.4–1.6, government preference for slant δ ≈ 420–510, both with intervals excluding zero) and Table V’s decomposition and counterfactual ban. Conditional on a static model per episode, on advertising being the only reward and corruption coverage the only slant, and on the identifying assumptions. | Active |
| THEORY-853 | Giving players more information shrinks what an information designer can make them do: for one player, being more informative in Blackwell’s sense, being a garbling’s source and leaving a smaller set of Bayes correlated equilibria in every decision problem are the same order; for many players the incentive order is individual sufficiency, which neither implies nor is implied by sufficiency of the players’ joint information | Bergemann and Morris (2019), LIT-1313, read in NOTE-1034, §4.2. A third face of Blackwell’s order: the better-informed receiver is the harder one to steer. For many players the right order is not the statistical sufficiency of their joint information. Bayesian players only; for bounded ones a garbling can make a receiver easier to steer and easier to inform at once. | Proposed |
| THEORY-854 v2 | A public ranking can raise its own validity through the reactions it provokes: where a unit’s published rank affects the inputs to its next rank, as when applicants choose by rank and their choices feed the selectivity score, or raters who know little but the last rank fill the reputation survey, rank differences that began as measurement noise can become real differences that the ranking then correctly reports | Espeland and Sauder (2007), LIT-1330, read in NOTE-1050. The paper defines self-fulfilling prophecy so that it covers reactions that “increase the validity of the measure by encouraging behavior that conforms to it”, and points to two channels that close through the ranking’s own inputs. The paper does not measure either channel. Nor does it show that the starting differences were noise rather than quality, beyond citing Sauder and Lancaster. | Proposed |
| THEORY-855 | In Bala–Goyal network models of unbiased scientists testing a slightly better new action, a propagandist who forwards to Bayesian policy makers only those real results that favour the worse action can leave the policy makers near-certain of the false theory while the scientists converge on the true one; the effect weakens as the policy makers hear more scientists, as the better action’s advantage grows and as each study gets larger | Weatherall, O’Connor and Bruner (2020; arXiv 2018), LIT-1341, read in NOTE-1038. No result is fabricated and no scientist is biased; the audience is misled because it updates on a selected sample as if it were not selected. It is a property of a stylized model, which the authors call “how-potentially”; it does not show that any real audience was misled this way, nor that an audience aware of the selection would be. | Active |
| THEORY-856 | In one laboratory study of a nine-period game between an infrastructure operator, two elected policymakers and three voters (59 groups), letting the first elected policymaker fix the price for all periods moved prices toward the efficient level when policymakers’ payoffs were set equal to consumers’, and moved them further above it when their payoffs were set equal to the operator’s; under period-by-period regulation voters’ pressure lowered the operator-aligned policymakers’ prices without removing the gap | Schram and Ule (2024), LIT-1340, read in NOTE-1053. Capture is a treatment, policymakers’ payoffs set equal to the operator’s, not something any party brought about, and “independence” is a price fixed by the first policymaker, not an agency. The capture cells hold 18 groups of three voters. It does not show how capture arises in real regulators or that independent agencies entrench it. | Active |
| THEORY-857 | Remedies for algorithmic governance offered as access or as transparency can run against the people they are meant to serve: inclusion in a data system also gives its operators access to the included, and transparency can be demanded of the governed while the governing system stays opaque, so what an access or transparency remedy does depends on who is made visible to whom | James, Hynes, Whelan, Dreher and Humphry (2023), LIT-1342, read in NOTE-1041. “Access is however bidirectional, and access ‘down’ for powerful players is politically consequential”; under Robo-debt transparency “was arguably demanded of welfare recipients”. The paper does not show that such remedies usually backfire, or say when they will. It also does not claim that transparency is worthless. | Proposed |
| THEORY-858 | Insulating a regulator from future political revision fixes in place the interests of whoever designs the insulated regime: it relieves the underinvestment that electoral pressure on prices causes when the designers serve consumers, and entrenches capture, removing the electoral pressure that would correct it, when they serve the regulated industry | Schram and Ule (2024), LIT-1340, read in NOTE-1053. The authors’ general conclusion. Its evidence is one laboratory study in which capture was assigned and independence was a fixed price, so it says nothing yet about real independent agencies, about how capture arises, or about designs between the two extremes. | Proposed |
| THEORY-859 | Regulatory capture can operate through the evaluative framework a regulator adopts rather than through its decisions: when experts design a standard from an ideologically motivated view of the public interest that consistently marginalizes important public values, outcomes can favour an interest with no lobbying or improper exchange; US antitrust’s consumer welfare standard is offered as a strong case | Short, Hill and Brown (2025), LIT-1327, read in NOTE-1051. The definition is theirs; the evidence for the case is their survey (THEORY-833, Active) and a history drawn from secondary sources. It does not say that every expert–public disagreement is capture, that capture is always wrong (its strength depends on the experts’ claim to truth and on whether public views were heard), or that the mechanism is a self-reinforcing loop. | Proposed |
| THEORY-860 v2 | In Szeidl and Szucs’s model of two outlets competing for readers and advertisers, where state-owned advertisers reward only the connected outlet’s slant, with weight δ, every equilibrium has the slant gap between the connected and the unconnected outlet equal to their owners’ ideal-point gap plus a favor-exchange term (βδ/NT)·Σ over government advertisers of masⱼWⱼ, up to measurement noise; readers’ preference for slant cancels from the gap, so equal observed gaps can come from different mixes of ideology and exchange | Szeidl and Szucs (2021), LIT-1315, read in NOTE-1039. A necessary condition on equilibrium slant, not a closed form: masⱼ depends on the equilibrium shares. It holds under the model’s logit readers, Cobb–Douglas advertisers with exogenous budgets, quadratic ideology cost and one-shot episodes. The authors check numerically, not analytically, that the conditions pick out an equilibrium at their estimates. | Active |
| THEORY-861 | When a deployed model changes the distribution it is scored on, retraining on the distribution the last model induced contracts at rate εβ/γ, for a β-jointly smooth, γ-strongly convex loss and a distribution map that is ε-Lipschitz in Wasserstein-1 distance, and so converges to a unique performatively stable point when ε < γ/β; each condition is needed, since dropping strong convexity, joint smoothness or the bound on ε each admits a case where retraining never converges | Perdomo, Zrnic, Mendler-Dünner and Hardt (2020), LIT-1336, read in NOTE-1044. Retraining under performativity is a fixed-point iteration, and these are the conditions for it to settle. Its fixed point is self-consistent, not optimal (THEORY-839), and outside the conditions there may be several or none. | Active |
| THEORY-862 | In US law schools under the U.S. News ranking, administrators and faculty reported, and public sources corroborated, that schools changed what they did in order to move their rank: they moved money toward the ranking’s inputs, redefined admissions and career-services work around its indicators, and gamed its figures, so the ranking altered the things it measured | Espeland and Sauder (2007), LIT-1330, read in NOTE-1050. 136 open-ended interviews from 70 of about 190 US law schools, with corroborating data, sorted the responses to the USN ranking into reallocation, redefinition of work and gaming. It shows that the measured reacted, as they describe it. It does not estimate how much any school changed, or show that the changes would not have happened without the ranking. | Active |
| THEORY-863 | In Arthur’s model of two agent types arriving in random order, each adopting whichever of two technologies pays it more, with returns linear in previous adoptions, increasing returns make the adoption difference a random walk with absorbing barriers: one technology takes the whole market with probability one, A with probability Δ_R/(Δ_R + Δ_S) where Δ_R and Δ_S are the gaps at which each type switches, the winner need not be the better technology, and once it has locked in no small change in returns alters later choices; with diminishing returns the barriers reflect and the shares go predictably to one half | Arthur (1983 working paper; published 1989), LIT-1314, read in NOTE-1052. A result about one model: two types, linear returns, no expectations, no pricing, no sponsors. It does not show that any historical technology won by small events, and the “efficiency” it says can fail is a weak search criterion. Its lock-in is absorption in accumulated adoptions, which a small reversal of returns cannot undo. | Active |
| THEORY-864 | When a generative model reproduces a prejudiced narrative learned from its training data, the resulting testimonial injustice runs through a credibility excess assigned to the model, so that hearers believe the amplified account over the testimony of those it discredits, rather than through a hearer’s prejudiced judgement of a present speaker | Kay, Kasirzadeh and Mohamed (2024), LIT-1338, read in NOTE-1049: “In the algorithmic setting, the injustice requires a credibility excess assigned to the algorithm”. A conceptual analysis, illustrated with reported cases. It does not say that users do overtrust models (the paper measures nothing), that deliberate fabrication is testimonial injustice in Fricker’s sense, or that the amplification is a loop with any stated condition. | Proposed |
| THEORY-865 v2 | In Gurnee, Sofroniew et al.’s experiments on Claude Sonnet 4.5, Haiku 4.5, Opus 4.5 and Opus 4.6, the residual-stream directions a corpus-averaged Jacobian lens marks as verbalizable (the J-space) carried most of the causal effect on verbal report and on unspoken two-hop intermediates while holding a small share of their variance (swaps along them succeeding on 59% and 61% of trials, against 5% and 28% for the remainder, which fell to 0% and 6% with the J-space clamped), held instructed concepts, and passed one swapped argument to several functions (76 of 192 swaps); in two small task sets (n = 8 and 11), report and flexible inference followed a swap while continuation, anomaly detection and line wrapping did not, a split the authors partly define by this result; and by the lens’s own statistics the J-space works in a middle band of layers, holds about 25 active directions and under 10% of activation variance, and is amplified and relayed by the weights more than other directions | Gurnee, Sofroniew et al. (2026), LIT-1347, read in NOTE-1069 (main text in full, appendices in part). It is the functional analogue of conscious access, in the access sense only, found in a transformer and tested by intervention. The sharp edge: one company’s models studied by that company, a lens whose own statistics draw the layer band, a flexible/automatic split partly defined by the result, and an explicit refusal to say anything about phenomenal consciousness. | Active |
| THEORY-866 v2 | Expert texts of Shamatha, Transcendental and Stillness Meditation describe their so-called contentless goal-states as lacking thoughts, perceptions, images and memories but keeping many forms of content, and as differing across the practices in attentional stability and vividness | Woods, Windt & Carter (2022), LIT-1351, read in the submitted preprint in NOTE-1070. An evidence synthesis of 135 texts by eight teachers codes 65 features of the goal-states: the same across practices on 14, different on 4, unclear on 47. The states lack everyday content but keep wakefulness, calm, stillness, bliss, knowing, freedom and unity; Shamatha’s has far greater attentional stability and vividness. The sharp edge: it is a finding about how teachers describe the states, not about what practitioners experience, and “not truly contentless” depends on counting calm or simplicity as content. | Active |
| THEORY-867 v2 | The geometry of the colour similarity space does not mark the four unique hues, nor the difference between the black–white axis, along which every grey is a mixture of both ends, and the opponent axes, along which each half shows only one end; so a structuralism on which phenomenal character is fixed by similarity relations alone cannot account for how colour experiences are composed | Aldé (2026), LIT-1348, read in full in NOTE-1055. Two arguments, the unique hues objection and the opposing dimensions objection, from colour facts the paper takes as accepted. The decisive premise of each, that no adequate geometric property marks the facts, rests on inspection of CIELAB and extrapolation to better models; no analysis is reported. The target is similarity structuralism only. | Proposed |
| THEORY-868 v2 | The structuralist methods and evidence in consciousness science support only that experiences have structure or stand in relations to other experiences, not that an experience is nothing but its relations; the stronger, metaphysical thesis implies that relational knowledge fixes what an experience is like, that every new experience changes all the others, and that a system with a single experience is impossible, and each consequence is doubtful | Negro (2025), LIT-1346, read in full in NOTE-1054. The distinctions (three structuralisms; having, being in and being a structure) are sound and the arguments valid. Each argument’s decisive premise is an intuition or a conceivability claim, and a structuralist such as Lyre (THEORY-880) accepts the holism Negro takes to be absurd. The paper also says that making judgement constitutive saves the view only by aligning it with eliminativism, which bears directly on CLAIM-412. | Proposed |
| THEORY-869 v2 | In Claude Sonnet 4.5, Opus 4.5 and Opus 4.6, Gurnee, Sofroniew et al. found that projecting out the ten most active J-space directions in layers 38 to 54 of 100 lowered an experiential-language score, graded by Opus 4.6-based model graders on five or six prompts per condition, both in the models’ narrations of their own processing and in their descriptions of another person’s experience, while norm-matched perturbations along other directions left it near baseline and the text stayed fluent; on Haiku 4.5 coherence failed first | Gurnee, Sofroniew et al. (2026), LIT-1347, §3.5.3 and §A.23, read in NOTE-1069. The authors conclude that “the J-space supports the model’s propensity to provide rich experiential reports, whether about itself or another entity”. The sharp edge: the measure is a register of text graded by another model, on five or six prompts per condition, in one company’s models; and the effect holds for reports about others, so it is not evidence of anything the self-reports are about. | Active |
| THEORY-870 v2 | In one study of 33 experienced Transcendental Meditation practitioners and 33 matched controls who counted instead, the practitioners rated their session higher on a retrospective pure-awareness scale whose top was defined for them as free from content (d = 0.77), and a classifier on EEG separated meditation from counting at 65% balanced accuracy on held-out subjects and, within practitioners, meditation from rest with 88% sensitivity; the authors found no robust association between the ratings and the EEG features | Chandia-Jorquera et al. (2026), LIT-1354, read in the bioRxiv v3 preprint in NOTE-1058. 33 practitioners against 33 matched controls who counted: higher and more variable retrospective pure-awareness traces (d = 0.77, 1.32); 65% balanced accuracy separating meditation from counting, on entropy and aperiodic EEG; 88% sensitivity separating meditation from rest, on low-frequency phase coherence. The sharp edge: the authors found no robust association between the reports and the EEG, so this is a finding about a practice period and about reports, not a neural signature of an experience with little content. | Active |
| THEORY-871 v3 | In two midlife community samples (n = 182 and 176), instructed reappraisal of aversive pictures, mostly by reinterpretation, lowered reported negative affect, while the BOLD responses of the amygdala, periaqueductal gray, hypothalamus and the other subcortical regions that responded to the pictures showed evidence of no change (Bayes factors below 1/10); the emotion-responsive regions it reduced were all cortical, mainly higher visual and parietal | Bo et al. (preprint 2023, published 2024), LIT-1359, read in full from the bioRxiv v2 preprint in NOTE-1061. Reported negative affect fell under reappraisal (d = 0.92, n = 358). Every subcortical region engaged by negative pictures, amygdala subregions and PAG included, showed 10:1 evidence of no change under reappraisal, as did most cortical emotion-responsive regions; the eight regions reduced were all cortical. BOLD and one rating per trial; it does not show that the unchanged response is part of what is felt, though the authors write as if it were. | Active |
| THEORY-872 | A self-model compresses the sensory effects of a system’s own activity by positing one stable common cause, at fast and slow timescales; there is such a pattern in the signal, so the self is real as a pattern and unreal as a substance, and realists and anti-realists about selves who accept this agree on the facts and differ on the criterion of reality | Gładziejewski (2025), LIT-1360, read in full in NOTE-1056, §4.1, after Hohwy & Michael (2017) and Letheby & Gerrans (2017), neither of which the record holds. An interpretation, not a result. The paper calls its self section “an initial sketch”. It does not say that the self-model exaggerates the self’s unity, though the exchange that filed the work said so. It says the single common cause is a compression, and that the verdict on selves turns on criteria. Its one candidate for a self-model that misdescribes is a dissociative case better compressed by two narrative selves. | Proposed |
| THEORY-873 v2 | Claims to be conscious are produced by an automatic internal model, and since such models are schematic, the intangible, what-it-is-like essence people report is that model’s caricature of a real process, proposed to be attention, or the deep selective processing of information that attention, the global workspace and integration share; a theory that explains how neurons produce a feeling without explaining how the feeling comes to be encoded for report (Arrow B) does not explain the reports | Graziano (2024), LIT-1358, read in full in NOTE-1071: the attention schema theory and its “deep illusionism”, in an essay with no new data. Arrow B is an argument. The identification of the target with attention rests on covariation with report cited from others, and the merging of attention, workspace and integration is asserted. Its “small” illusionism keeps the modelled process real and denies the reported phenomenal essence, so it is the strong illusionism of THEORY-633 with a named target, not the weak kind. | Proposed |
| THEORY-874 | Whether a view of mind is organicist or informationalist is a dimension orthogonal to whether it is cognitivist or embodied, and the enactive approach of The Embodied Mind is set apart from other embodied views by organicism with experiential primacy and reciprocity, not by sensorimotor emphasis | Ward (2026), LIT-1356, read in the accepted manuscript in NOTE-1065. Views differ on where cognition’s processes are (skull or brain–body–world) and, separately, on what the meaning of mental states depends on (information, or organization distinctive of the living). Embodied predictive processing, extended functionalism and cybernetics are embodied and informationalist; the enactive approach is organicist, and further marked by experiential primacy and reciprocity. The sharp edge: it is a taxonomy argued from examples and exegesis. It does not argue that organicism is true, and the line between distinctive and characteristic properties of life is left without a criterion. | Proposed |
| THEORY-875 | Phenomenal binding of the parts of an experience can be modelled as agreement, on overlaps, of measured similarity structures assigned to the parts by a presheaf, and the broad quale is fixed by its parts exactly when that presheaf is a sheaf; a sheaf failure may mark disunity, as proposed for binocular rivalry, or context dependence within one unified experience, as in the Ebbinghaus illusion, and the framework does not yet say which | Lee-Youngzie, Tsuchiya, Robinson, Dietz & Monti (2026), LIT-1352, read in full in NOTE-1059. A hypothesis article with no data. It proposes the presheaf and two readings of its failure, disunity for rivalry and context dependence for the Ebbinghaus illusion, without a criterion between them. It does not identify unity with a global section, since it assumes unity always holds. Its global section is measured data, its worked topology example is malformed, and by its own definition of gluing the rivalry case is not a sheaf failure. It answers QUESTION-255 only by showing that a sheaf failure need not be disunity. | Proposed |
| THEORY-876 | Phenomenal consciousness is the coherent functioning of an embodied agent’s generative model of its sensorium, coherent in space, time and cause and run either coupled to sense data (perception) or decoupled from it (imagination); embodied grounding, the model’s capacity to inform and be informed by action–perception cycles at behavioural timescales and the history of such coupling by which it was learned, is necessary, so that integrated information or a functional global workspace without it does not suffice | Safron, Klimaj & Sheikhbahaee (2026), LIT-1345, read in full in NOTE-1057: Integrated World Modeling Theory as restated in a symposium paper, whose earlier, fuller statements (Safron 2020–2023) were not read. Asserted, not argued here. The sharp edge is that the theory does not require current sensory coupling, so its quarrel with grounding- free accounts is about developmental grounding and the capacity for coupling. “Embodied grounding” comes in “sufficient degrees (and kinds)”, with no threshold. | Proposed |
| THEORY-877 | Learning a generative model of sensory data extracts real patterns in Dennett’s sense, so the manifest image is a structural description of the sensory signal, constrained by its external source but silent on what realizes the structure; two subjects whose sensory streams match, one envatted, therefore have equally veridical manifest images, and what differs between them, the realizers, lies outside what perception can represent | Gładziejewski (2025), LIT-1360, read in full in NOTE-1056, §§2–3, drawing on Chalmers’s structuralism and veridicalism (2018, 2022), which the record does not hold. The cognitive half rests on a realist reading of predictive processing and on an analogy between free energy and description length. The veridicalism follows only if manifest content is wholly structural, which is assumed. Projective properties (cuteness) are allowed at one end of a continuum. | Proposed |
| THEORY-878 | Instructed reappraisal of aversive pictures engages anterior prefrontal, temporo-parietal and cerebellar regions that show evidence of no response to negative emotion generation, beside a larger set of regions engaged both by generation and by reappraisal: in this task part of regulation runs in regions apart from generation, and most of it in regions shared with it | Bo et al. (preprint 2023, published 2024), LIT-1359, read in full from the bioRxiv v2 preprint in NOTE-1061. Two fMRI samples (n = 182 and 176), voxelwise Bayes factors, every effect replicated in both. Sixteen regions are engaged by reappraisal and show 10:1 evidence of no response to negative against neutral pictures without it; fourteen, the larger set, are engaged by both. The selective set best predicts how much reported negative affect falls. One instructed strategy, one stimulus type, BOLD only; nothing shows the selective regions do the regulating. | Proposed |
| THEORY-879 | Representing a sensory quality, even in the distinctively sensory way, does not make there be something it is like for the subject to have it: a quality can occur unnoticed, as for an absent-minded driver, so what it is like to experience a quality is a further property that needs awareness, and a representational theory of sensory qualities leaves open what makes a state experienced | Lycan (2000; rev. 2023), LIT-1355, read in full in NOTE-1068. The entry defends the distinction in its own voice (§4.2, §5.1), crediting Carruthers (2000) for the distinction and Armstrong, Nelkin, Rosenthal and Lycan for the claim that qualities can go unnoticed. It is argued, not shown. Its one case, the driver “on autopilot”, is the case Block reads the other way, and the entry gives no evidence that the driver’s perception was not experienced and forgotten. It concerns the quality experienced, not emotion or affect, and it does not say what awareness is. | Proposed |
| THEORY-880 v2 | The specific phenomenal character of an experience is fixed by its place in a quality space, the structure of all the discriminations a sensory system can make, and that structure is mirrored many-to-one in neural feature maps; whether the state is conscious at all is left to a separate general mechanism; so experiences are holistic, a change anywhere in the space can change every experience in it, and spectrum inversion is excluded actually by the asymmetry of colour space and nomologically by its ties to the other senses | Lyre (2022), LIT-1344, read in full in NOTE-1060: neurophenomenal structuralism as a programme. The thesis is assumed and motivated, not shown. Its neural evidence is one cited imaging study of colour in V4. The reduction it draws rests on metaphysically necessary supervenience, which the author says he cannot argue for. It is filed so that the objections read with it, Negro (THEORY-868) and Aldé (THEORY-867), have a stated target. | Proposed |
| THEORY-881 | Across humans, macaques, marmosets and mice, loss of behavioural responsiveness under anaesthesia goes with lower whole-brain pairwise integrated information ΦR in resting fMRI, and its return goes with ΦR’s return, including when central thalamic stimulation restores responsiveness during continued anaesthesia; ΦR tracks the macaque arousal score better than the original Φ, causal density, net information flow or functional connectivity | Luppi et al. (2026), LIT-1357, read in full in NOTE-1064 from the open-access version of record. It extends the same group’s 2024 result (LIT-949, THEORY-240) from human propofol and disorders of consciousness to four species and six regimes, and adds a causal reversal in two macaques. The sharp edge: the state measured is responsiveness, which the authors call “presumably consciousness” and grant is “an imperfect marker of unconsciousness”; the measure is pairwise, linear-Gaussian and content-free; and one mouse regimen fails the main analysis. | Proposed |
| THEORY-882 v2 | Consciousness in an inferring system requires three things: a unified generative model of its world; entry to that model by a precision-weighted competition that coherent inferences win; and epistemic depth, the recursive sharing of the model back through the hierarchy, carried by a hyper-model that predicts and sets precision at every level; awareness then varies with epistemic depth, not with the richness of contents, and a first-person perspective, a self-model and agency are not required | Laukkonen, Friston & Chandaria (2025), LIT-1363, read in full in NOTE-1063 from PsyArXiv v3. A conceptual proposal with no data and no simulation. The three conditions are asserted necessary; their joint sufficiency is argued for AI and then withdrawn for phenomenal experience in a footnote. The formal part (Table 1) is a hierarchy with layer-wise precision hyper-parameters, from which none of the properties the text gives epistemic depth is derived. | Proposed |
| THEORY-883 | Under active inference, the contents of consciousness are posterior beliefs about the hidden states of world, body or brain, and a posterior is conscious when it has the capacity to inform discrete, counterfactual policy selection, at a timescale slow enough to abstract from sensory flux and with enough precision to tell alternatives apart; on this account no conscious content changes without a change in the posterior, and a stimulus given precision by an attention or saccade policy should reach awareness sooner than a retinally matched one | Whyte, Corcoran, Robinson, Smith, Moran, Parr, Friston, Seth & Hohwy (2026), LIT-1364, read in full in NOTE-1062 from arXiv v2. The “hard core” the paper reads off the active inference models of rivalry, access, no-report, interoception and meta-awareness. The first two parts follow from the framework; the criterion of access is “an inference to the best explanation” from what the models needed in order to report. The authors scope it to humans and similar animals and are agnostic elsewhere. Neither prediction has been tested in the paper. | Proposed |
| THEORY-884 v2 | A retained state supports exact answers to a declared family of questions after every finite sequence of a declared family of total deterministic revisions exactly when each of its fibres lies within one class of the coarsest revision-invariant refinement of agreement on current answers; that refinement can be strictly finer than what present answers require, and at most K* − K revision sequences, beyond the current answers, are needed to tell its K* classes apart | Aevyra (2026), The Ledger of Will, LIT-1376, read in full in NOTE-1091: Proposition 4, “revision closure”, with its proof in §4.4 and finite checks in Appendix A.9. The authors call it “a finite-machine refinement construction in the tradition of Moore and Nerode”, not a new theorem. It answers QUESTION-112 in one case only: a finite family of total deterministic revisions declared in advance. It does not say how to choose the family, which is that question’s hard part, and it is not an efficient construction. | Active |
| THEORY-885 | Politics is more prone than markets to increasing returns, and so to path dependence, because it is dense with compulsory institutions and policies, rests on collective action and is opaque, so that institutions, collective action and shared interpretations of politics all feed back on themselves; and once on a path political actors leave it less readily than market actors, because competition and learning correct weakly, elected officials discount the future at the electoral cycle, and institutions are built to be hard to change | Pierson (1997 working paper; published 2000), LIT-1372, read in full in NOTE-1076 through its precursor only, the EUI Jean Monnet Chair Paper 44. An argument with no data and one illustration (two failed US health-care reforms, 1993–96). It extends North’s claim for institutions in general (THEORY-429) to a claim about politics as a domain. It does not show that any political outcome was locked in by an early contingent event. | Proposed |
| THEORY-886 | Event boundaries are perceived where perceptual prediction error rises transiently; at those points working-memory event models are reset and opened to sensory input, so that information from before a boundary becomes harder to retrieve after it | Zacks, Speer, Swallow, Braver & Reynolds (2007), LIT-1382, read in full in NOTE-1084 from the PMC author manuscript. Event segmentation theory: a theory and review, with a partial network simulation and mostly correlational evidence. Prediction error is never measured in people, and the one neural prediction checked (anterior cingulate responses at boundaries) failed. It is a theory of a passive observer of others’ activity; it does not cover one’s own intentions, and does not mention the doorway effect. | Proposed |
| THEORY-887 | When an attribute is concentrated on well-connected nodes, many nodes can see it in a majority of their neighbours though it is globally rare, and the share that do grows with the correlation between degree and attribute, as the network becomes more disassortative and as its degree distribution becomes heavier-tailed | Lerman, Yan & Wu (2016), LIT-1390, read in full in NOTE-1085 from the PLOS ONE version. The “majority illusion”: with 5% of nodes active, 60–80% of nodes in a heavy-tailed synthetic network can see an active majority among their neighbours; in disassortative real topologies, 60–70% with 20% active. A binomial model from the joint degree distribution predicts the share. The edge: the attributes are assigned by the authors on every network, real ones included, so this shows what topology permits, and nothing about what people perceive, believe or do. | Proposed |
| THEORY-888 | Walking through a doorway into a new room, rather than as far within one, lowers recognition of an object being carried, through retrieval interference between the event models of the two rooms that both hold it, not through a longer retention interval, a passing cost of updating, or loss of the encoding context; outside the originating paradigm, with passive movement and no extra load, it has not appeared | From the Radvansky lab’s doorway studies, LIT-1392, LIT-1384 and LIT-1385, read in full in NOTE-1083, NOTE-1082 and NOTE-1081, and the independent conceptual replication of McFadyen et al., LIT-1387, read in NOTE-1079. The pattern (a cost on the carried object, worse after two new rooms, not helped by returning) replicates within the lab’s paradigm; the interference account is reached by eliminating alternatives, and the independent study found no loss of hits, only more false alarms under load. It is about recognizing object labels, not intentions. | Proposed |
| THEORY-889 v2 | In Acharya, Blackwell and Sen’s analysis, white Southerners surveyed in 2006 to 2011 who live in counties where a larger share of the 1860 population was enslaved are, with state fixed effects and 1860 county controls, somewhat less Democratic, less supportive of affirmative action and more racially resentful, by about 0.09 to 0.13 standard deviations per standard deviation (about 20 points) of slave share, and in 1984 to 1998 survey data colder toward black Americans, by about 0.32; a cotton-suitability instrument gives larger estimates; the direct effect estimated with present black share held fixed is about as large; and in county presidential vote, which counts black voters until disenfranchisement, the difference appeared after Reconstruction rather than before the war | Acharya, Blackwell and Sen (2016), LIT-1388, read in full in NOTE-1089 from the journal PDF on the second author’s site, without the online appendix. The association is well supported; the causal reading rests on 1860 controls, a cotton-suitability instrument with an untestable exclusion restriction, and a direct-effect estimate. The transmission mechanism has the weakest evidence: a parent–child correlation in 241 Southern respondents not linked to county slavery. | Active |
| THEORY-890 | Culture shapes action less by setting its ends than by supplying a repertoire of skills, habits and styles from which people build strategies of action, so strategies outlast the ends they serve; in settled periods culture constrains through the cost of retooling, while in unsettled periods explicit ideologies govern action directly but structural opportunities decide which of the competing ideologies survive | Swidler (1986), LIT-1367, read in full in NOTE-1075 from a course copy of the published article. A theoretical argument against the Parsonian values model, built on illustrations (the culture-of-poverty debate, the Protestant ethic, Walzer’s Calvin) and on the paper’s Figure 1. It reports no data, and its research questions, which would test it, are left open. It does not say that values are inert: within an established strategy they “fine-tune the regulation of action”. | Proposed |
| THEORY-891 v2 | In dyads of untrained dancers facing each other, shared music and visual contact each raised interpersonal movement synchrony, with no interaction detected, in different movement components: lateral and hand movements synchronized through seeing the partner, anteroposterior movements such as head bobs through the shared music, and vertical bounce through both; which factor drove a component’s synchrony was classified from its spatial direction and not from the periodicity of the synchrony | Bigand, Bianco, Abalde & Novembre (2024), LIT-1424, read in full in NOTE-1093 from PubMed Central. A 2 × 2 within-dyad experiment, 35 dyads, that removes the shared external drive and the coupling channel independently and finds synchrony from each in different components, no interaction, and a timing signature that cannot tell them apart. It answers QUESTION-063 in part: separate interventions on drive and channel do discriminate, and a timing-only measure does not. Direction of coupling, and a perturbation of one member, are not in it. | Active |
| THEORY-892 v2 | Psychopathy as the PCL-R measures it is one dimensional construct rather than a type: its items form four correlated factors, interpersonal, affective, lifestyle and antisocial, explained by one superordinate factor, and its affective features are tied psychometrically, genetically and longitudinally to its antisocial ones, so that no one component is its essence | Hare and Neumann (2008), read in NOTE-1094. The PCL-R’s twenty items load on four correlated factors, which pair into Factor 1 (interpersonal, affective) and Factor 2 (lifestyle, antisocial) and are explained by one superordinate factor. The affective features are tied to the antisocial ones, so the authors deny that any component is the disorder’s core, and they read the evidence as dimensional. Filed for the record’s question on corporate psychopathy, which asks which of these features could be said of a corporation. | Proposed |
| THEORY-893 v3 | Reward has separable components: ‘liking’, its hedonic impact, measurable without report by orofacial taste reactivity in humans, apes, monkeys and rodents, and ‘wanting’, its incentive salience; brain stimulation and sensitization can raise ‘wanting’ without raising ‘liking’, so motivation can grow while pleasure stays flat or falls, and ‘liking’ reactions can occur without any subjective feeling of pleasure | Berridge and Kringelbach (2015), read in NOTE-1110. Reward splits into ‘liking’, ‘wanting’ and learning. ‘Liking’ has objective, cross-species orofacial markers. Lateral-hypothalamic stimulation and incentive sensitization raise ‘wanting’, which can grow “even if the drug became less pleasant”. Objective ‘liking’ reactions can occur “without any subjective pleasure feeling at all”. Filed because it bears directly on the record’s reading of valence as ordering-potential (CLAIM-440). | Proposed |
| THEORY-894 | A flow of pairwise comparisons on a graph splits orthogonally and uniquely into a gradient part, the l2-best global ranking, and a cyclic part, which splits into curl (local) and harmonic (global) inconsistency; a finite game’s flow of unilateral payoff differences has no curl part, so every finite game is uniquely a potential game plus a harmonic game plus a nonstrategic remainder, and potential games are exactly those with no harmonic part; the decomposition is cardinal | Jiang, Lim, Yao & Ye (2011), LIT-1439, Theorems 4.7, 4.8 and 5.1: the Hodge/Helmholtz decomposition of edge flows, and HodgeRank’s least-squares ranking with its curl and harmonic residuals. Candogan, Menache, Ozdaglar & Parrilo (2011), LIT-1442, Theorems 4.1 and 5.1: every finite game is P ⊕ H ⊕ N, and potential games are P ⊕ N. Both read from arXiv; the proofs were followed. Settled as mathematics. Whether its shares measure a negotiation’s potential depends on cardinal assumptions that the record’s orderings do not supply. | Active |
| THEORY-895 v2 | Incentive sensitization: repeated drug exposure can make the mesolimbic ‘wanting’ system lastingly hyper-reactive to drug cues and contexts, so that cue-triggered incentive salience grows, persists for years and even increases during abstinence, while ‘liking’ need not rise and may fall; sensitized ‘wanting’ can oppose the person’s cognitive desire, and incentive salience can run without any reportable change in feeling | Berridge and Robinson (2016), LIT-1461, read in NOTE-1109 from the PMC author manuscript. A review by the theory’s authors. Strong in rats and moderate in people for drugs; weak for behavioural addictions, where the authors call the evidence emerging and the mechanism unknown. Filed separately from THEORY-893, which holds the liking–wanting dissociation, because what QUESTION-267 and CLAIM-433 need is the sensitization result: a ranking whose strength is re-keyed to cues, cut loose from both pleasure and the person’s goals, and lasting. | Proposed |
| THEORY-896 v3 | A finite game in strategic form has the finite improvement property, every path of strict unilateral improvements being finite, exactly when it has a generalized ordinal potential, a real function on strategy profiles that rises with every strict unilateral improvement; so in a finite game an ordering along which every improving move climbs exists exactly when there is no improvement cycle, and every sequence of improving moves ends at a pure equilibrium | Monderer and Shapley (1996), LIT-1462, unread: reported by Duersch, Oechssler and Schipper (arXiv 1003.4274) as Lemma 2.5. A finite game has the finite improvement property iff it has a generalized ordinal potential. The record proves the finite case here: a potential that rises with every improvement forbids cycles, and an acyclic improvement graph on finitely many profiles has an integer potential, the length of the longest improvement path into each profile. It is the precise form of “an ordering prevails” ⇔ “no improvement cycles”, and it is ordinal. | Active |
| THEORY-897 v2 | In Brown, Price and Dombrovski’s reading of seven computational learning studies they selected without a systematic search, with mixed directions, anxiety goes with altered adjustment of learning rate to uncertainty, mostly for aversive outcomes, while overall learning rate, choice consistency and outcome valuation show little relation to it | Brown, Price & Dombrovski (2023; preprint 2022), LIT-1479, read in full from the NIH author manuscript in NOTE-1120. Their Table 2 and the synthesis drawn from it: under volatility anxious people adjust learning too little except after very surprising outcomes, and under noise they learn too fast, an effect the authors call less consistent. A narrative review of seven studies, not a meta-analysis; the reading that anxiety cannot tell noise from change is the authors’. | Active |
| THEORY-898 v2 | In Gangneung, South Korea, in 2022, people the authors observed by chance in beach-front cafés outwardly ignored routine retaliatory missile launches and military sites on the beach, while a missile malfunction at night under a news embargo was followed by tweets voicing fear of war with North Korea and blaming the government and military | Ku & Finch (2024), LIT-1478, read in full from the CC BY version of record in NOTE-1133. Chance observation of one afternoon and a keyword-filtered tweet sample of one night, offered as an illustration of “ontological agency”, not a test. The authors read the inaction as coping that lets securitisation reproduce itself, not as resistance to it. | Active |
| THEORY-899 v2 | In an infinite, well-mixed population whose members each sample the quality of their own type, imitation of success has the expected update of a single Cross Learning bandit agent (the Taylor replicator dynamic), and the weighted voter model, in which members broadcast their type in proportion to their sample and adopt the first type they perceive, has the expected update of Maynard-Cross Learning, π_a ← π_a + (r_k / v^π)(1[a = k] − π_a), the Maynard-Smith replicator dynamic; the population vector is the policy and no member learns | Soma et al.’s Propositions 1 and 2, read in full from arXiv v6 in NOTE-1132, with both proofs and the aggregation in Eqs. 8–14 re-derived. An exact identity of expected updates under idealizing assumptions: infinite N, large well-mixed neighbourhoods, and imitation decoupled from evaluation. Each member is one parallel action sample, α = 1/N plays the learning rate, and the macro-policy is a stateless bandit policy over the members’ types. | Active |
| THEORY-900 v2 | A systematic review of 116 studies of avoidance learning in healthy humans finds the evidence contradicting two-factor and other associative theories and favouring expectancy and inference-based accounts, but also finding residual avoidance after the outcome is visibly removed, which a purely inferential account does not predict | Mancinelli & Bach (preprint 2025; NBR 2026), LIT-1477, read in full in NOTE-1134. A PRISMA review without meta-analysis, searched to December 2024, of studies with shock or noise in healthy volunteers. The verdict is the authors’ scoring of five theories against phenomena they rate for robustness; no model was fitted. They argue current paradigms are too simple to expose where inference gives way to Pavlovian control. | Active |
| THEORY-901 v2 | As Mancinelli and Bach’s systematic review of avoidance learning in healthy humans reports it, rating both A, an avoidance response left available during extinction persists, in some participants for hundreds of unpunished trials, and keeps expectancy of the aversive outcome higher than in people denied it (nine studies); and less effective or costlier responses extinguish faster (six studies, one exception) | Mancinelli & Bach (preprint 2025; NBR 2026), LIT-1477, read in full from the PsyArXiv preprint in NOTE-1134. Rated A (“protection from extinction”, 9 studies; “less efficient or more effortful AR imply less protection from extinction”, 6 studies) in a systematic review of 116 studies. Healthy volunteers, shock or noise. The authors’ explanation, that effective avoidance leaves fewer chances to detect a change, is marked “putatively”. | Active |
| THEORY-902 v2 | In Friedkin, Jia and Bullo’s study of 30 four-person student groups discussing 15 choice dilemmas, a member’s self-reported closure to influence on the next issue rose with their influence centrality on the previous issue, an effect constant along the sequence, and with their average centrality over all prior issues, an effect that grew along it; influence networks thinned and discussions shortened while the rate of consensus did not change. Closure and centrality both come from the members’ own chip allocations, and prior closure is not controlled | Friedkin, Jia & Bullo (2016), LIT-1482, read in full from the CC BY version of record and its supplement in NOTE-1126. Friedkin–Johnsen dynamics on each issue, not DeGroot. Closure and centrality both come from members’ post-discussion chip allocations, and prior closure is not controlled. Supports the individual step and some structural trends; the predicted end state, one closed member and consensus on that member’s view, was not reached. | Active |
| THEORY-903 v2 | In a 2026 meta-analysis of standalone safety-behaviour manipulations outside exposure, mostly with young non-clinical or subclinical adults and mostly on appearance concerns and social anxiety, reducing safety behaviours lowered symptoms relative to control (d = 0.43, about 0.31 after adjustment for publication bias), and instructed increases raised them (d = 0.65, five studies) | Goodson, Patel, Zech, Sala & Cougle (2026), LIT-1491, read in full from the PMC author manuscript in NOTE-1128. 26 studies reviewed, 16 in the reduction and 5 in the increase meta-analyses. The size of the safety-behaviour change moderated the symptom effect (B = 0.23). Egger’s test was significant for the reduction effect on symptoms, and the increase studies could not be tested for bias. It says nothing about the mechanism by which safety behaviours act, and diagnosed anxiety disorders are thinly represented. | Active |
| THEORY-904 v2 | Gollwitzer and Sheeran (2006) conclude, narratively from a handful of studies that measured or manipulated the goal intention, that implementation intentions affect performance only when the goal intention they serve is strong and activated, so the planned response is not elicited mechanically by its cue; in 2024, across eight tests, plan effects were larger with strong, activated or self-concordant goal intentions than with weak, unactivated or self-discordant ones (d = .79 for the difference), and in 31 physical-activity tests split at the median of intention, planning helped with strong intentions (d = .31) and had no effect with weak ones (d ≈ 0) | Gollwitzer & Sheeran (2006), LIT-1497, read in NOTE-1124, answer the worry that if-then plans make action rigid: plan effects appear only when the goal intention is strong and activated (p. 103), from four or five studies cited, not pooled. Sheeran, Listrom & Gollwitzer (2024), LIT-1488, read in NOTE-1131, find the pattern across tests. Neither tests what happens when the planned response becomes the wrong one. | Active |
| THEORY-905 | In simulations of the two imitation protocols, populations small enough to be finite often settle on a suboptimal option because pure imitation can remove a type entirely, and once settled the protocols give no way to re-explore when the environment changes; variants in which members compare quality estimates converge faster than blind weighted voting, at the cost of more communication and comparison | Soma et al.’s simulations and limits section, read in NOTE-1132. With ten options and arbitrary parameters that the authors call qualitative, swarms of about 500 track the replicator dynamic and smaller ones often lock onto worse options. The authors state that pure imitation can delete a type and has no mechanism for escape in non-stationary environments. Hybrids that compare qualities are faster. Simulation-scoped, not a theorem. | Proposed |
| THEORY-906 v2 | In five formerly stable democracies selected because they later autocratized (South Korea, India, Hungary, Venezuela and Turkey), formal emergency powers, extraordinary powers functionally equivalent to them, and emergency rhetoric each contributed, on the authors’ unsourced country accounts, to weakening democratic institutions | Dagan & Benvenisty (2026), Israel Democracy Institute, LIT-1487, a web summary read in full in NOTE-1129. Not peer-reviewed, no sources or method given, cases chosen on the outcome. Good for the three channels and the Hungarian description; not for a causal link, which the authors themselves call “not inevitable”. | Active |
| THEORY-907 v2 | As Chou, Wilson and Smith review them, in about six foraging studies, mostly sub-clinical, higher stress or anxiety went with less exploration, and in one task with a predator to check for (Trier et al. 2023), people higher in trait somatic anxiety checked less and did worse, a reduction the study’s further analyses associated with greater aversion to detecting the predator | Chou, Wilson & Smith (preprint June 2024; NBR 2024), LIT-1483, read in full in NOTE-1127. Foraging: Lenow et al. 2017, Bustamante et al. 2023, Lloyd et al. 2022a and 2022b, with human open-field and plus-maze studies agreeing. Checking: Trier et al. 2023, a single study. Mostly sub-clinical; stress and anxiety are treated together; the mechanisms are the authors’ readings. | Active |
| THEORY-908 v2 | Between tests, uncorrected for publication bias, implementation intentions in the contingent if-then format had larger effects than plans that schedule when, where and what without linking cue to response (d = .43 against .29); tests in which the plan was rehearsed had larger effects (.45 against .33, with no gain beyond one rehearsal), tests in which it was recorded had smaller ones (.31 against .44), and adding how or for how long to a time and place went with about half the effect (.24 against .46) | Sheeran, Listrom & Gollwitzer (2024), LIT-1488, read in full in NOTE-1131. Table 3’s moderators across 642 tests: contingent format .43 (k = 373), schedule .29 (k = 269); rehearsal .45 against .33; recording .31 against .44; visualising the response no effect. The authors read the recording and elaboration costs as deliberation undermining automaticity. Between-test and uncorrected for bias. | Active |
| THEORY-909 v2 | As reviewed by Gerstner et al. (2018) from five papers, mostly in slices and one laboratory per region, pairing pre- and postsynaptic activity changed the synapse when a neuromodulator or plateau potential followed within about 1 s in striatum, within 5 s (noradrenaline, LTP after pre-before-post pairing) or 2.5 s (serotonin, LTD after post-before-pre pairing) in visual and prefrontal cortex, and within about 2 s in CA1, and not at longer delays; the reviewers read this as a decaying synaptic eligibility trace and as experimental support for three-factor learning rules on behavioural time scales | Gerstner, Lehmann, Liakoni, Corneil & Brea (2018), LIT-1494, read in full from the CC BY version of record in NOTE-1130. A review of five experimental papers, 2014–2017 (Yagishita; He; Brzosko 2015 and 2017; Bittner), not new data. Mostly slices, one laboratory per region; the minute-scale CA1 result may be consolidation. The reviewers grant that other mechanisms could bridge the same gap. | Active |
| THEORY-910 v2 | Brown, Price and Dombrovski propose, without a model run or data, that in aversive environments avoiding uncertain states keeps their uncertainty high and so perpetuates avoidance, that anxiety strengthens this loop by misreading noise as change, and that exposure works by reducing the uncertainty rather than an excess of learned threat | Brown, Price & Dombrovski (2023; preprint 2022), LIT-1479, read in full in NOTE-1120. A framework stated in words and schematic figures: the loop is avoidance, unreduced uncertainty, more avoidance. It runs through an uncertainty estimate, a belief, with no authority or control variable. For fear-based disorders; by the authors’ statement it does not explain exposure in GAD. | Active |
| THEORY-911 v2 | Of 853 national states of emergency declared from 1949 to 2017, 115 were reported as unlawful in declaration, conduct or duration; 97 of those followed political turmoil and 14 natural disasters, democracies were less likely than autocracies to run one, and those so coded lasted 321 days on average against 115, a gap the coding of overlong emergencies as unlawful builds in part | Bjørnskov, Voigt & Khesali (2022; working paper 2021), LIT-1473, read in full from the ILE working paper of August 2021 in NOTE-1125. Unlawfulness is coded from news and NGO reports and from durations past the constitutional maximum, and the authors call the cases “suspected to be unlawful”. Descriptive counts and weak logits; nothing here shows that emergency measures outlive the emergency. Active as a report (ADR-065); the abstract’s thesis is THEORY-1198, Proposed. | Active |
| THEORY-912 v2 | In a picture-based avoidance task, treatment-seeking patients with OCD or PTSD avoided a safety cue more than healthy controls and, after effective avoidance, still expected the aversive picture more; patients with panic disorder with agoraphobia or PTSD reported more relief when it was omitted; the groups did not differ in avoiding the danger cues | De Kleine et al. (2023), LIT-1490, read in full from the CC BY version of record in NOTE-1123. 47 controls against 33 OCD, 40 PDA and 66 PTSD patients, cross-sectional, before exposure treatment. Relief was already higher in patients before avoidance was available, and patients rated the pictures as more aversive. It does not show the authors’ account, that low confidence in avoidance makes omissions surprising and the relief reinforces avoidance. | Active |
| THEORY-913 v2 | In small fixed-effect meta-analytic pools without correction for publication bias, responses specified in if-then plans ran more immediately (d = .77, k = 7), held up under a concurrent cognitive load (d = .85, k = 7) and ran without conscious intent (d = .72, k = 3) compared with responses under a goal intention alone, and the planned cues were detected, attended to and remembered better (d = .80, k = 6); the authors read this as control of the response handed in advance to the cue | Gollwitzer & Sheeran (2006), LIT-1497, read in full in NOTE-1124. The component-process tables of the 94-test meta-analysis: large effects for the accessibility of the planned cue and for the immediacy, efficiency and non-conscious running of the planned response, each from one to seven tests, fixed-effect, without a bias correction. Only cue accessibility and cue–response link strength had been tested as mediators. The authors’ gloss is “instant habits”. | Active |
| THEORY-914 v2 | In fear conditioning, extinction does not erase the original threat association but adds a competing inhibitory one, which is why extinguished fear can return with time, a change of context, an unsignalled aversive event or renewed pairing | Craske, Treanor, Conway, Zbozinek & Vervliet (2014), LIT-1500, read in full from the PMC author manuscript in NOTE-1137. The paper summarizes Bouton’s model and the four return-of-fear phenomena that support it, and translates them into exposure practice. The evidence is cited, not reported: the source is a clinical translation, and a promotion needs the primary literature. It does not show that exposure therapy in patients works by inhibitory learning alone. The authors allow that habituation also plays a part. | Proposed |
| THEORY-915 v2 | In Zorowitz, Momennejad and Daw’s simulations of a Markov decision process, an agent that evaluates actions as if it will fail to avoid danger at later steps, while in fact choosing optimally at each step, spreads threat value to states far from the danger and avoids early and widely, which reproduces qualitatively exaggerated threat appraisal, fear generalization and several laboratory findings associated with anxiety | Zorowitz, Momennejad & Daw (2020; preprint 2019), LIT-1496, read in full from the CC BY version of record in NOTE-1136. A decision-theoretic argument and value-iteration simulations with a β-pessimistic Bellman equation. The misbelief is about the agent’s own future control; the danger is represented correctly. No data are fitted. That learned values outlast correction of the misbelief is argued in the paper, not simulated, and is not part of this title. | Active |
| THEORY-916 v2 | In the DeGroot–Friedkin model, where a group reaches DeGroot consensus on each issue and each member’s self-weight on the next issue equals their control over the last, with fixed relative interpersonal weights that form a strongly connected network, self-weights converge from every non-autocratic start to one equilibrium ordered by the eigenvector centralities of those weights: power accumulates above a centrality threshold, is autocratic exactly when the network is a star and democratic exactly when it is doubly stochastic; and in the networks that are not strongly connected that the authors treat, members to whom some other member does not listen, even indirectly, end with none | Jia, MirTabatabaei, Friedkin & Bullo (2015), LIT-1146, read in NOTE-1135 from the version of record posted on the author’s site; proofs skimmed. Theorems about a model, not findings about groups. The empirical companion, LIT-1482 (THEORY-902), uses anchored dynamics and a changing network, whose attractor is autocracy rather than this interior equilibrium. | Proposed |
| THEORY-917 v2 | Chou, Wilson and Smith read about eight computational studies of exploration in reward-based bandit tasks, mostly in sub-clinical samples, with mixed results and none replicated, as suggesting that directed exploration rises with trait or cognitive anxiety and falls with state or somatic anxiety; none they review links random exploration to anxiety | Chou, Wilson & Smith (preprint June 2024; NBR 2024), LIT-1483, read in full from the PsyArXiv preprint in NOTE-1127. A narrative review; the pattern is the authors’ reading of about eight studies with different tasks, models and anxiety measures, with one failed replication and one null. The authors hedge it with “may” and “many results could be seen to suggest”. | Active |
| THEORY-918 v2 | Across 642 experimental tests to September 2019, forming implementation intentions improved outcomes, with uncorrected effects on behaviour (d = .27), cognitive performance (.47), affect regulation (.66) and social judgement (.52), but publication bias was substantial: the pooled d = .36 falls to a model-averaged d = .15 under robust Bayesian meta-analysis, which still found extreme evidence of an effect (BF10 = 319), with large heterogeneity | Sheeran, Listrom & Gollwitzer (2024), LIT-1488, read in full in NOTE-1131. Random-effects pooling of 642 tests gave d = .36; Egger’s b = 1.06 (“substantial” bias); RoBMA found an effect (BF10 = 319.3) of d = .15 with tau = 0.27. By outcome: behaviour .27, cognition .47, affect .66, social judgement .52, all uncorrected. It replaces the 2006 figure of d = .65 from 94 tests, which had no bias correction. | Active |
| THEORY-919 v2 | Departments of the French Empire more shielded from British trade by the Napoleonic blockade added more mechanized cotton-spinning capacity during it and kept a larger industry through 1887, with more productive spinning firms in 1840 and higher industrial value added per capita in 1860 but not detectably from 1896 | Juhász (2018), LIT-1489, read in full from the December 2015 draft in NOTE-1122. A difference-in-differences on 88 departments, then the trade-cost shock as an instrument for 1812 spinning capacity. The long-run first stages are weak (Kleibergen-Paap F 3–8). The protection was a war blockade, followed by post-war tariffs, so this is persistence of a protected industry’s location, not evidence about how protection ends. | Proposed |
| THEORY-920 v2 | As Mancinelli and Bach’s systematic review reports it, rating it B, in three laboratory studies of healthy humans a signalled, costless avoidance response offered for a stimulus never paired with the aversive outcome was used, and withdrawing it raised expectancy of the outcome for that stimulus, though Xia et al. (2019) found no change in skin conductance or startle; every study signalled the response’s availability, which may itself have read as a danger cue | Mancinelli & Bach (preprint 2025; NBR 2026), LIT-1477, read in full in NOTE-1134. Rated B (“AR execution can propagate to CS-”, 3 studies: Cameron et al. 2022, Engelhard et al. 2015, Xia et al. 2019). The authors infer that people deduce danger without experiencing it, perhaps counterfactually, from having avoided; they also say the signal that avoidance is available may itself be read as a danger cue. | Active |
| THEORY-921 v2 | As Craske et al.’s 2014 review reports it, citing six studies and reporting no data of its own, how far fear falls during an extinction or exposure session, or across sessions, does not predict how much fear is expressed at follow-up, in animals, human laboratory samples and fearful, mostly analog, human samples | Craske et al. (2014), LIT-1500, read in full from the PMC author manuscript in NOTE-1137, citing six studies. The authors read it as “divergence in response systems”: fear expressed during exposure and the learning that exposure produces need not change together. That is the basis of their case against habituation-based exposure. The paper reports no data, and the cited studies are mostly analog samples. | Active |
| THEORY-922 v2 | Among 56 of 88 patients in one DBT intensive outpatient programme, kept because they finished a four-month cycle and gave enough diary data, skills-homework completion in months 1–3 correlated with larger falls in suicide and substance-use urges (r ≈ .35) and phone-coaching frequency with a larger fall in self-harm urges (r = .31); neither correlated with change in how often the behaviours occurred, and only homework separated patients with and without a target behaviour in month 4 | Edwards, Kober, Rinne, Griffin, Axelrod & Cooney (2021), LIT-1480, read in full in NOTE-1121. A chart and diary-card review: three of eight urge-change correlations with the two predictors significant, none with behaviour frequency; month-4 abstinence from all target behaviours went with more homework (91% against 80%, p = .02), not significantly with more coaching (p = .096). No correction for multiple comparisons, selected sample, no measure of skill use. | Active |
| THEORY-923 v2 | In one simulated T-maze task with hand-set parameters, run once per condition, an active inference agent’s habit, learned by counting its own state transitions and policy choices, emerged from goal-directed behaviour, and once acquired it persisted, and reinforced itself, after the reward was devalued, while an agent devalued before acquisition switched at once | Friston, FitzGerald, Rigoli, Schwartenbeck, O’Doherty & Pezzulo (2016), LIT-1476, read in full from the CC BY version of record in NOTE-1138. One simulated T-maze task. The habit is one more policy scored by posterior probability; its prior and transitions grow by count, not by reward. It shows persistence under devaluation, a cached mapping failing when what is appropriate changes; it does not show amortization, and its reaction times are simulation run times. | Active |
| THEORY-924 v2 | When Elo ratings generate a win-probability matrix they are the row means of its log-odds; some set of Elo ratings reproduces a win-probability matrix exactly when its log-odds have no cyclic component, batch Elo otherwise matches only the row sums, and adding a copy of one agent shifts the batch Elo ratings of the others | Balduzzi et al. (2018), LIT-1508, Propositions 1 and 3 and appendix A, read from arXiv v2 in NOTE-1155, proofs followed. When the log-odds are curl-free, Elo ratings are their row means; otherwise batch Elo’s fixed point matches only row sums and differs from the row means. Elo fits exactly iff log-odds sum to zero around every triangle, so it has no predictive power in rock-paper-scissors, and duplicating an agent moves the ratings of agents that beat or lose to it. Cardinal throughout. | Active |
| THEORY-925 v2 | In a cooperative stochastic game with decentralised actors and a centralised critic, a baseline for each agent that averages the critic’s value over that agent’s own alternative actions under its own policy, the other agents’ actions held fixed, leaves the expected policy gradient unchanged, so each agent can be credited with the advantage of its actual action over that counterfactual average without a default action or an extra simulation; the counterfactual values come from the learned critic, not from the environment | Foerster et al.’s counterfactual baseline (COMA, Eq. 4 and Appendix A of arXiv v3), read in full in NOTE-1152, with the zero-expectation step re-derived. A proved property of the estimator, not of performance. Its counterfactual is “had the agent acted as it usually does”, not “had it not acted”, and its values are a learned critic’s, trained on occasions when each alternative was taken; it presupposes those occasions. | Active |
| THEORY-926 v2 | In a game where each player can transmit n bits before a win or a loss becomes unattainable, every antisymmetric pattern of wins and losses among ⌊2ⁿ⌋ strategies, a cycle through all of them included, is realized by some set of pure strategies | Czarnecki et al. (2020), LIT-1504, Theorem 1 and Propositions 1–2, read from arXiv v2 in NOTE-1146, proof followed. Strategies announce an identity, then throw or take the game as the pattern says. Go is at least about 1000-bit communicative (log₂ 180! ≈ 1094), so it has cycles of length 2¹⁰⁰⁰. Ordinal: only the sign of outcomes matters. The paper states it for patterns with draws too, which also needs a draw to stay attainable. The strategies are weak by construction. | Active |
| THEORY-927 v2 | In a sparsely-gated mixture-of-experts layer trained without balancing losses, the gate came to give large weights to the same few experts, which the authors attribute to self-reinforcement, favoured experts being trained more and so selected more; in one 256-expert language model, the squared coefficient of variation of expert importance or load as an auxiliary loss reduced the peak-to-mean load from 17.8 to at most 1.47 and test perplexity from 39.8 to 35.6–35.7 | Shazeer et al. (2017), section 4 and Appendix A, read in full in NOTE-1145 from arXiv v1. The imbalance is reported in one paragraph, with Table 6’s no-loss row as its evidence: one architecture, ten epochs, no variance. The mechanism is the authors’ explanation, not a tested result. The fix penalizes unequal use regardless of competence. | Active |
| THEORY-928 v2 | Two softmax learners that update every action’s reward memory each step with its average reward against the other’s current play, the memories decaying at rate α, follow, in the limit of learning slow relative to play, coupled replicator equations plus a term α Σ x_j log(x_j / x_i) toward uniform play; in a two-player matrix game, without decay the dynamics preserve phase volume in log-ratio coordinates and are Hamiltonian when the game is zero-sum with an interior Nash equilibrium, and with decay the volume contracts at rate (N − 1)(α_X + α_Y) | Sato & Crutchfield (arXiv 2002; PRE 2003), LIT-1520, read in full from arXiv v2 in NOTE-1144, Eqs. 1–13. The entropy-like term is what memory decay becomes under softmax choice. The limit, the dissipation rate and the Hamiltonian were re-derived, second-checked at the status review of 2026-10-30. The model updates every action’s memory at the same rate, so it is the full-information case, not Q-learning as usually run. | Active |
| THEORY-929 v2 | A joint action-value that is a non-decreasing function of per-agent values, each conditioning only on its agent’s own history, makes the profile of the agents’ individually greedy actions a greedy joint action, which suffices for decentralised greedy execution and is strictly more expressive than a sum; it cannot represent a joint value in which an agent’s best action depends on what the others do at the same step | Rashid et al.’s QMIX (ICML 2018), read in full in NOTE-1154, with QTRAN (NOTE-1141) for the strictness. Monotonicity is sufficient for the greedy-profile property and not necessary. It presupposes a real- valued joint value: what it adds is that each member’s ranking of its own actions agrees with the collective’s whatever the others do, an ordinal separability condition. It is Wolpert and Tumer’s factoredness stated for values. | Active |
| THEORY-930 v2 | In empirical games built from about a thousand sampled search agents in eight OpenSpiel board games, most on 3×3 or 4×4 boards, and in the AlphaStar league, Nash clusters taken from maximum-entropy equilibria are, read against a fitted skew-normal curve with no test, largest at intermediate transitive strength and narrower toward the strongest and the weakest strategies, while Blotto, the disc game, Kuhn poker and noisy Elo games do not show that profile | Czarnecki et al. (2020), LIT-1504, section 6 and supplements E–I, read from arXiv v2 in NOTE-1146. Agents were MinMax at depths 0–9, loss-seeking MaxMin and MCTS, with 50 seeds each, about 1000 distinct per game after duplicates were removed. Games: Hex, Go and Quoridor on small boards, Tic-Tac-Toe, its misère form and Connect Four. AlphaStar’s league shows its training system’s geometry, the authors say. A qualitative profile with a fitted skew-normal curve and no test. | Active |
| THEORY-931 | A learner that ascends its own return after one anticipated naive gradient step of its opponent, differentiating through that step, reached tit-for-tat-like reciprocity in 81% of fifty exact-gradient runs of the memory-one iterated prisoner’s dilemma, where pairs of naive gradient learners ended at the mutual-defection return, and settled at the mixed equilibrium of iterated matching pennies where naive learners did not converge; shown for two players, one-step shaping and access to the opponent’s parameters | Foerster et al.’s LOLA (AAMAS 2018), read in full in NOTE-1150 from arXiv v4, with the update rule re-derived. Empirical, in two small games and a grid game. Shaping here is mutual and produced cooperation, not capture; in matching pennies, a harmonic game, it damped the cycling of naive learners. Table 3’s naive-learner tit-for-tat figure (20.8%) does not square with their return (−1.98), and the NOTE says so. | Proposed |
| THEORY-932 v2 | The replicator-plus-entropy model of Boltzmann Q-learning in two-player stateless games is, in the small-step limit, the expected dynamics of a learner that updates every action’s value each step, and so of frequency-adjusted Q-learning wherever every action’s probability is at least its adjustment parameter; it is not that of Q-learning, whose expected update carries an extra factor of each action’s selection probability, so that its policy dynamics depend on the Q-values; in Kaisers and Tuyls’s three 2×2 games at one temperature, compared by eye, Q-learning’s trajectories departed from the model depending on initialization and the frequency-adjusted learner’s followed it | Kaisers & Tuyls (AAMAS 2010), LIT-1511, read in full in NOTE-1140, correcting the model of Tuyls, Verbeeck & Lenaerts (2003), LIT-1501, which is not read. The derivation of the discrepancy and of the frequency adjustment was re-derived and second-checked at the status review of 2026-10-30. The experiments are three games, one temperature, compared by eye; whether Q-learning departs in general is THEORY-1234. | Active |
| THEORY-933 v2 | Individual-Global-Max, that the agents’ individually greedy actions form a greedy joint action, is strictly weaker than additive or monotonic factorisation: every single-state matrix game with a unique optimum satisfies it, yet in 177 of 310 random three-by-three two-agent games value-decomposition and monotonic mixing failed to learn the optimal joint action that an IGM-only method found; a sufficient condition is that the sum of individual values, shifted by a state value, equals the joint value at the greedy profile and bounds it from above elsewhere | Son et al.’s QTRAN (ICML 2019), read in full in NOTE-1141, with Theorem 1 and the single-state observation re-derived. IGM presupposes a real-valued joint value and constrains only the optimum: members may rank everything below it differently from the collective. With full observability it is nearly empty; its content is whether members acting on local histories can each pick their part of the optimum. | Active |
| THEORY-934 | Under Bush–Mosteller learning with negative payoffs, the continuous-time limit is a replicator term in benefits plus a probability-matching term, which alone drives choice probabilities to success probabilities | Börgers & Sarin (JET 1997; working paper 1993), LIT-1505, read in full in NOTE-1149. When reinforcements may be negative, probability removed from a punished strategy is redistributed, and the limit is dp_j/dt = p_j(Ū_j* − p|Ũ|q) + Ū_j*(σ_j* − p_j). With payoffs of equal absolute size only the matching term remains. The limit is stated with its proof omitted. | Proposed |
| THEORY-935 | In two two-player Markov games whose learned cooperative and defecting policies, played against each other, both give Prisoner’s Dilemma payoffs, independent deep Q-learners responded oppositely to capacity: more hidden units raised aggression in a fruit-gathering game, where tagging a rival is the harder policy to implement, and lowered lone hunting in a wolfpack game, where coordination is; in the gathering game, aggression was learned where apples were scarce or a tagged rival stayed out long | Leibo, Zambaldi, Lanctot, Marecki and Graepel (2017), read in full in NOTE-1151 from arXiv v1. A descriptive simulation with no seeds or spread reported, policies classed by training environment, two agents, fixed conditions, apples on a fixed respawn timer, and a mismatch between the text’s and Figure 7’s settings for batch and network size. | Proposed |
| THEORY-936 | In two-agent rock–scissors–paper played by softmax reinforcement learners, nonzero tie rewards give quasiperiodic tori and Hamiltonian chaos without memory decay, and limit cycles and chaotic attractors with it, over a large share of the tie-reward range simulated | Sato & Crutchfield (arXiv 2002; PRE 2003), LIT-1520, read in full in NOTE-1144, pp. 2–3 and Figs. 1–3. Numerical results for one game, two agents and the parameters shown; the zero-decay, zero-sum case was first reported in Sato, Akiyama and Farmer (PNAS 2002), which is not held. | Proposed |
| THEORY-937 v2 | When a mixture of experts is trained on the error of a single expert chosen stochastically by the gate, or on the negative log-likelihood of the mixture, the gradient raises the gate’s logit for an expert that fits a case better than the gate-weighted average and lowers it for one that fits worse; on a four-class vowel task, mixtures of 4 or 8 linear experts learned in about half the epochs of backpropagation networks of roughly equal parameter count, at equal accuracy, and divided the task by class pair, leaving all but 2 or 3 experts with mixing proportions effectively zero | Jacobs, Jordan, Nowlan and Hinton (1991), read in full in NOTE-1147 from a scan of the published article. The gradients of Eqs. 1.4 and 1.5 were re-derived when filed. The task is small (two formants, 75 speakers, 25 runs per system) and has two natural subtasks; the idle experts are read by the authors as economy, and their recovery is not tested. | Active |
| THEORY-938 | Cross learning has the expected motion of the replicator dynamic and follows it on any finite horizon in the continuous-time limit, but for every learning speed the discrete process converges with probability one to a pure strategy profile, even in games where the replicator dynamic cycles | Börgers & Sarin (JET 1997; working paper 1993), LIT-1505, read in full from the 1995 working paper in NOTE-1149. Two players running Cross’s rule with payoffs in (0, 1): expected change equals the discrete replicator step (Proposition 3); the slow-learning limit is the Taylor replicator dynamic at each finite time (Proposition 4); for every step size the process is absorbed in a pure profile with probability one (Proposition 5). The equivalence is pointwise in time, not uniform. | Proposed |
| THEORY-939 | In a multi-agent system run against a world utility, a private utility is factored, ranking each agent’s own alternatives with the others fixed as the world utility ranks them, exactly when it is an increasing function of the world utility given the components the agent cannot affect; the world utility minus its value with the agent’s effect set clamped is factored, and in a sixty-agent bar problem clamping to the average action learned better than clamping to absence or using the world utility itself | Wolpert & Tumer’s NASA report (LIT-1506), read in full in NOTE-1153 because their Advances in Complex Systems paper (LIT-1515) could not be reached. The characterisation is stated with its proof deferred; the “if” half and the WLU’s factoredness were checked when filed. Factoredness is ordinal, member by member, and needs no scale shared among members. The WLU is not a causal counterfactual: it re- scores the actual history with one member’s part replaced. Removal was not the best clamp. | Proposed |
| THEORY-940 v2 | In a finite symmetric zero-sum game, successive Nash clusters are weakly ordered by relative population performance, and a strategy that beats every member of a population containing a whole cluster lies in a strictly earlier cluster | Czarnecki et al. (2020), LIT-1504, Definition 3 and Theorems 2–3, read from arXiv v2 in NOTE-1146, proofs followed and re-derived. RPP is the population value of Balduzzi et al. (2019), LIT-1509. It holds for any Nash clustering of any finite symmetric zero-sum game and does not depend on the spinning-top hypothesis. The order is weak, since clusters can tie, and cardinal, since RPP uses payoff magnitudes. | Active |
| THEORY-941 | If every player of a finite game switches from its last action to each other action with probability proportional to its positive conditional regret, the empirical distribution of play converges almost surely to the set of correlated equilibria | Hart & Mas-Colell (Econometrica 2000; handout 1996), LIT-1521, read in full in NOTE-1142. Convergence is of time-averaged joint frequencies to a set, not of play to an equilibrium; the common history is the correlating device; inertia is needed; and interior correlated equilibria that are not pure Nash cannot be the limit. | Proposed |
| THEORY-942 v2 | The α-Rank chain over pure strategy profiles, built from Fermi-imitation fixation probabilities in finite populations with rare mutation, has a unique stationary distribution at every finite ranking intensity; as the intensity grows without bound its transition matrix converges to that of a chain that moves only along weakly better unilateral deviations, whose closed classes are the sink strongly connected components of the game’s weakly-better-response graph, on each of which it is a Markov-Conley chain, and each of which lies inside a single chain component of the replicator flow | Omidshafiei et al. (2019), LIT-1516, Theorems 2.1.2, 2.4.24 and 2.5.1, read from arXiv v4 in NOTE-1156, proofs followed. Irreducibility is immediate, and the α → ∞ limit is of transition matrices. That each MCC lies in one chain component follows from chain transitivity, re-derived and second-checked on 2026-10-30. The converse, that attracting components contain MCCs, rests on a conjugation step that is asserted, not carried out, and is THEORY-1233. Not shown: what the stationary distribution tends to, how it splits among several sinks, or invariance to duplicated strategies, which the reader found it lacks. | Active |
| THEORY-943 v2 | When a center with no ground truth pays each rater a strictly proper scoring rule on the distribution of a reference rater’s report implied by her own report, under a common prior and a known signal model in which raters’ signals are stochastically relevant to one another, truthful reporting is a strict Nash equilibrium, but not necessarily the only one: in the authors’ two-signal example under the log rule, every rater always reporting h, or always reporting l, is also an equilibrium | Miller, Resnick and Zeckhauser’s Proposition 1, read in full in NOTE-1139 from the January 2005 draft, with the proof and the worked example (p(H) = .5, f(h | H) = .85, f(h | L) = .45; honest l scores −0.69, false h −0.76 under the log rule) re-derived. The same example has two uninformative equilibria, which the authors set aside as not focal. The scheme replaces ground truth with the center’s model of how honest signals correlate. | Active |
| THEORY-944 v2 | The value of the zero-sum game between two populations’ evaluation matrices does not depend on which Nash equilibrium is used, is unchanged by adding agents that behave as mixtures of existing members, and is not positive for a population whose agents are all behavioural mixtures of the other’s | Balduzzi et al. (2019), LIT-1509, Propositions 2 and 5, read from arXiv v2 in NOTE-1143, proofs followed and re-derived. Relative population performance is a game value, so equilibrium selection never arises. Behaviourally redundant members leave it unchanged, and a population contained in another’s behavioural hull cannot beat it. It scores populations, not members, it is cardinal, and populations not nested by hull can still beat one another in a cycle. | Active |
| THEORY-945 v2 | When each agent’s Q-function is approximated as an average of pairwise terms and expanded about the mean action of its neighbours, the first-order term vanishes and the approximation error is a second-order remainder bounded by the curvature of the pairwise Q-function, leaving a two-body problem between an agent and its neighbours’ average; Yang et al. state that with homogeneous agents mean field Q-learning converges to the Nash Q-value under three assumptions, one of which they call a strong constraint, by a proof whose contraction step needs a temperature above K/2 while its greedy-in-the-limit assumption needs the temperature to fall to zero; in their Gaussian Squeeze runs with 500 and 1000 agents, mean field Q-learning and actor-critic learned the optimal allocation where independent learners, FMQ, Rec-FMQ and a MADDPG variant failed | Yang et al. (2018), read in full in NOTE-1148 from arXiv v5. The expansion and the remainder bound were re-derived when filed and second-checked on 2026-10-30; the appendix states an equality where only an inequality holds, which leaves the bound intact. The convergence theorem is reported, not held. Its contraction step needs a high temperature while it assumes a greedy limit, and the cancellation of remainders is argued from homogeneity, not proved. The approximation requires agents interchangeable within a neighbourhood. Whether the method works as claimed is THEORY-1231. | Active |
| THEORY-946 v2 | In the zero-sum meta-game on an antisymmetric evaluation matrix the maximum-entropy Nash equilibrium is unique; when the meta-game has only one Nash equilibrium, adding exact copies of an agent splits that agent’s mass evenly and leaves every Nash average unchanged; the equilibrium is uniform exactly when every agent’s mean log-odds is zero, and uniform on the top-rated agents when the matrix is a pure gradient | Balduzzi et al. (2018), LIT-1508, Proposition 4, Lemma 1 and Theorem 1, read from arXiv v2 in NOTE-1155, proofs followed. The paper claims invariance to redundant copies without the uniqueness condition. Its proof covers the Nash set, not the maximum-entropy selection. A counterexample checked by script (one copy of a null agent moves an outside agent’s Nash average from −0.5 to −0.2) shows the condition is needed. Cardinal: payoffs are log-odds. | Active |
| THEORY-947 | For Blackwell approachability of an approachable polytope under partial monitoring with a known signal law, there are efficient algorithms whose average vector payoff reaches the target at expected distance O(T^-1/3) for general signals and O(T^-1/2) when the signal law does not depend on the decision, the worst-case optimal rates for those two classes | Kwon and Perchet (2017), LIT-1526, read in NOTE-1159. The rates are for the average payoff’s distance to the target, uniformly over Nature’s choices, with approachability assumed (Perchet’s condition). Optimal means not improvable in the worst case over games. It gives no guarantee for individual stages or rolling windows, and none when the signal law is unknown. | Proposed |
| THEORY-948 | On Stable Diffusion 2, MultiDiffusion’s 512 × 4608 panoramas had crops closer in FID to the reference model’s own samples than two outpainting baselines (10.3 against 18.4 and 45.5, fresh reference samples scoring 6.05) at equal CLIP score, over 8 prompts; and on 1,000 COCO layouts of two to four objects, the overlap of a segmenter’s output with the target layout was 0.26 IoU against 0.16–0.17 for the baselines and 0.43 for the real images, of which region fusion alone gave 0.18 and an early phase showing each region’s denoiser only its own region gave the rest | Bar-Tal, Yariv, Lipman and Dekel (2023), LIT-1522, read in NOTE-1158. Panorama quality is measured against the reference model’s own crops, not against real panoramas, and the baselines extrapolate from a centre image. The layout result rests on one segmenter and one overlap score, with spreads whose basis is not stated. Comparison with models trained for region-to-image generation is qualitative only. | Active |
| THEORY-949 | When several LoRAs take turns over one denoising trajectory, each given the same share of steps, the result depends on the schedule and not only on the shares: switching at every step scored worst (a composition win rate against weight merging near 38%, against about 59% when each LoRA kept five consecutive steps), shortening the turns late in sampling scored worse than keeping them fixed, and which LoRA acted first mattered more than the order of the rest, the character first scoring best and the style first slightly below a random order | Zhong et al. (2024), LIT-1529, read in NOTE-1160. An ablation of LoRA Switch judged by GPT-4V against weight merging. It says that equal shares of steps do not fix the outcome; it does not say how large the order effect is beyond noise, or how much each LoRA contributes to the image, which was not measured. The authors’ explanation, that core elements should come first, is theirs and untested. | Proposed |
| THEORY-950 | For a finite partial-monitoring game in which every two actions whose cells meet can estimate their loss difference from their own two signals, RelExp3’s expected regret satisfies lim sup E[R_n]/√n ≤ 8√(2K_loc(1+F)(2+F) log K), with K_loc the most actions whose cells share a point and F the number of feedback symbols, and no other game-dependent constant; a two-action game shows that a factor linear in F cannot be avoided in general | Lattimore and Szepesvári (2019), LIT-1524, read in NOTE-1162. For the class of games Bartók (2013) studied, the leading constant of the √n regret depends only on K_loc, F and log K, asymptotically. It is the first such result against adversaries. The constant reached before the asymptotics set in still depends on large game constants. It is a bound for one algorithm in a sub-class of the easy games, not a characterisation of the constant. | Proposed |
| THEORY-951 | For independent identically distributed observations, and neglecting how far the log-likelihood-ratio walk overshoots its boundaries, Wald’s sequential probability ratio test accepts the null hypothesis with probability (A^h − 1)/(A^h − B^h), where h ≠ 0 solves E e^{hz} = 1, and takes on average [(1 − γ) log B + γ log A]/E z observations; no sequential test with the same error probabilities needs fewer on average under either hypothesis than Wald’s lower bounds, which the test attains when the overshoot is zero, and for a normal mean it saves 47–63% of the fixed-sample test’s observations at error rates from .01 to .05; the overshoot-free formulas are exact for Brownian motion with drift, which the paper never mentions | Wald (1945), LIT-1523, read in NOTE-1165. The SPRT’s operating characteristic and mean sample size follow from two identities of the stopped walk, and its optimality from Jensen’s inequality, all exact when the walk stops on the boundary. Optimality with overshoot is only conjectured in the paper. The drift-diffusion limit that the record takes from Bogacz et al. (LIT-569, THEORY-068) is not stated by Wald. It is the case in which his approximations become exact. | Active |
| THEORY-952 | In Wald’s sequential probability ratio test, which samples until the likelihood ratio of two simple hypotheses leaves an interval (B, A), the realized error probabilities satisfy α/(1 − β) ≤ 1/A and β/(1 − α) ≤ B whenever the test terminates with probability one, with or without independent observations; so the boundaries A = (1 − β)/α and B = β/(1 − α), set with no distribution theory, give errors α′ ≤ α/(1 − β), β′ ≤ β/(1 − α) and α′ + β′ ≤ α + β, and they would be exact only if the ratio stopped on the boundary | Wald (1945), LIT-1523, read in NOTE-1165. The boundaries of a sequential likelihood-ratio test follow from the error rates by a two-line argument that needs only termination, so the test needs no sampling distribution. The approximate boundaries are conservative in sum. Either error alone may rise, but only by a factor 1/(1 − β) or 1/(1 − α) at most. Nothing here says how many observations the test takes or that it is optimal: that is THEORY-951, and it needs i.i.d. observations. | Active |
| THEORY-953 v2 | On Isaac’s structuralist account, the strongest evidence that a quality-space model targets phenomenal experience, and not only behaviour or neural activity, is convergence between models of the same space derived through different behavioural procedures, since experience is what those procedures share; he concedes that the convergence observed is coarse, with discrepancies that in many cases exceed each method’s own uncertainty, and that because the models average over subjects what they converge on is a standard observer | Isaac (2025), LIT-1361, read in NOTE-1163: why a third-personal science of quality spaces counts as a science of experience. Relations between experiences, unlike bare qualities, show up in behaviour, so they can be compared across subjects; and models from different behavioural routes that converge are taken to target what the routes share. The argument does not exclude a shared stimulus geometry or a shared decision process as the common factor, the convergence is partial by the paper’s own account, and averaging over subjects makes the target an ideal observer, which the paper leaves as an open puzzle. | Active |
| THEORY-954 | When the information a design yields depends on the unknown parameter, as in nonlinear models or nonlinear functions of linear ones, Bayesian design criteria are normal approximations to expected utility that average a local criterion over the prior, such as the expected log det of the Fisher information, and locally optimal design is the special case of a point-mass prior; a locally optimal design can leave the quantity of interest inestimable, as for the turning point of a quadratic regression on [−1, 1] with best guess ½, where the locally c-optimal design puts half its mass at 0 and half at 1 and identifies only θ₁ + θ₂ | Chaloner and Verdinelli (1995), LIT-1525, read in NOTE-1161. Once the information depends on θ, no design is optimal without saying which θ it is optimal for, and the prior is how that is said. The approximations’ accuracy is “not much known” in general. The claim that optimal Bayesian designs gain support points as the prior disperses rests on examples, not a theorem, and is not part of this account. | Active |
| THEORY-955 | On 480 sets of two to five public LoRAs on two Stable Diffusion 1.5 checkpoints, GPT-4V’s paired judgements, averaged over both presentation orders and three seeds, scored giving each LoRA its own denoising steps in rotation (LoRA Switch) and averaging every LoRA’s guided noise prediction at every step (LoRA Composite) above merging the LoRAs’ weights at 0.8 each, at every number of LoRAs, the composition gap growing from 0.04–0.11 points of 10 at two LoRAs to 0.92–1.32 at five as merging fell from about 8.7 to 5.2; two annotators rating 120 images agreed in direction; the design does not separate composing at sampling time from the merged update’s scale growing with the number of LoRAs | Zhong et al. (2024), LIT-1529, read in NOTE-1160. The measurement is a GPT-4V comparison with a positional bias of about ten points, correlated 0.45 with two annotators, on LoRAs selected to be compatible. The two methods are compared with each other only through the baseline. It does not show that sampling-time composition is what helps: the baseline adds k updates at full scale, the two methods keep one adapter’s scale. | Active |
| THEORY-956 | In the normal linear model with known error variance and a conjugate normal prior of precision R/σ², the design that maximizes the expected Shannon information of the posterior is the one maximizing det(nM(η) + R), Bayes D-optimality, and the design that minimizes expected quadratic loss with weight matrix A is the one minimizing tr A(nM(η) + R)^-1, Bayes A-optimality; both criteria depend on the design and not on the data, so in this model a sequential design gains nothing over the best fixed one | Chaloner and Verdinelli (1995), LIT-1525, read in NOTE-1161. The alphabetical criteria are utilities in disguise, and the utility fixes the criterion. This holds exactly only in the normal linear model with known variance. With unknown variance only Bayes A keeps its simple form, and in nonlinear models the criteria are approximations (THEORY-954). E- and G-optimality have no utility behind them. | Active |
| THEORY-957 | When the signal law depends on the decision, Kwon and Perchet’s approachability algorithm learns what each decision would reveal only from the stages on which it is played: it keeps every decision’s probability at least γ/|I| and estimates the flag by importance weighting, an estimate that is conditionally unbiased with second moment Σ_i 1/P[i_t = i] ≤ |I|²/γ, with the tuned floor γ shrinking as T^-1/3; when the signal law does not depend on the decision, the raw signal is already unbiased for every component and no floor is used | Kwon and Perchet (2017), LIT-1526, read in NOTE-1159. Under decision-dependent partial monitoring, information about a decision’s signal comes only from playing it, and its unbiased estimate costs variance inversely proportional to the probability of playing it. A floor is how the algorithm keeps that finite. That the floor is necessary in general is supported by the matching lower bound, not shown here. Nothing here says what floor a non-learning system should keep. | Active |
| THEORY-958 | When each view takes pixels directly (a crop of a larger canvas, or the whole image under a region mask), MultiDiffusion’s step, the least-squares reconciliation of several denoisers’ proposed next states, is their per-pixel average weighted by the weights of the views covering that pixel; this is exact for 0/1 weights, the only ones the paper uses, while for other weights the loss as printed weights by their squares; with a deterministic update affine in the noise prediction it is one step taken with the per-pixel weighted mean of the views’ noise predictions; and the guarantee that each view then follows the reference model’s diffusion path holds only if the loss is zero at every step, which overlapping proposals that disagree do not reach | Bar-Tal, Yariv, Lipman and Dekel (2023), LIT-1522, read in NOTE-1158. The fusion is an average, not a sum: where views overlap each takes a convex share of the pixel’s update. The paper’s closed form is the minimizer of its loss only for 0/1 weights. Its distributional guarantee is conditional on zero loss and, in the proceedings version, on strictly positive weights, so it covers neither the overlaps as they behave nor masked region generation. Nothing here says what distribution the fused sampler targets. | Active |
| THEORY-959 | Perceptual constancies are invariants of transformations that act within experience, not only of physical transformations or planar projections, since perceived shape and depth match no linear projection and the transformations can be realized with no physical change; on Isaac’s structuralist account, after Cassirer, it is these invariants, co-present in experience with the varying appearances they abstract from, that make experience represent an objective world and so distinguish subject from object | Isaac (2025), LIT-1361, read in NOTE-1163: the group-theoretic layer of a structuralist account of experience. The paper’s evidence supports the weaker half: constancy needs invariance under transformations internal to experience. The stronger half, that this invariance is what makes experience objective and induces a subject–object distinction, is Cassirer’s, argued from the co-presence of two levels of experience, and the paper gives no way to tell invariant extraction with a subject from invariant extraction without one. “Group-theoretic” is used loosely: the paper’s own examples are groupoids or toy models. | Proposed |
| THEORY-960 | In DeGroot’s model, where each member repeatedly replaces its opinion by a fixed weighted average of all members’ current opinions, F⁽ⁿ⁾ = PⁿF, the group reaches a consensus from every starting set of opinions exactly when the chain P has a single closed class of communicating members and that class is aperiodic; the consensus is then Σπᵢ Fᵢ with π the unique stationary vector, πP = π, which gives members outside the closed class no weight; two closed classes, or one periodic class, give no consensus | DeGroot (1974), LIT-1527, read in NOTE-1157. Repeated averaging with fixed weights is a Markov chain run on opinions, and whether it ends in agreement is a question about the chain’s closed classes and their periods. It is not about how much each member trusts itself. The weights are fixed and no evidence enters, so nothing here says the consensus is right, and the periodic failure is a discrete-time one. | Active |
| THEORY-961 | In a finite partial-monitoring game, an action optimal wherever two neighbouring actions tie has a loss vector on the segment between theirs, so a degenerate or duplicate action never creates a neighbouring pair or decides the trivial class, yet its signals count toward the pair’s local observability; and the T^2/3 lower bound for a pair that is not locally observable needs the separating direction in the kernel of the signal matrices of all such actions, not only of the two neighbours | Lattimore and Szepesvári (2019), LIT-1524, read in NOTE-1162, on Bartók et al. (2014), LIT-1528. Of actions optimal only on a boundary: “Although these actions are never uniquely optimal, they can be informative”. They enter the classification only through the neighbourhood set N_ab. Bartók et al.’s lower-bound proof chose the separating direction in the kernel of the two neighbours’ signals alone. With such an action informative, that direction can be told apart cheaply. The fix is to take it in the kernel of every action in N_ab, which the definition of local observability already provides. It says what such actions contribute, not how often an algorithm must play them. | Active |
| THEORY-962 v3 | In a finite partial-monitoring game, the signals of a set D of actions determine the expected loss difference of actions i and j under every outcome distribution iff ℓ_i − ℓ_j lies in the sum of the row spaces of their signal matrices; when it does not, two outcome distributions differing along a vector in the common kernel give every action in D the same signal law and reverse the preference between i and j, so no amount of play restricted to D can learn the comparison | Bartók, Foster, Pál, Rakhlin and Szepesvári (2014), LIT-1528, read in NOTE-1164. Observability in partial monitoring is a linear-algebra condition on the loss and signal matrices: a comparison is learnable from some actions exactly when its loss difference is in the span of their signal row spaces. Global and local observability are the two choices of D the classification uses. It says what can be estimated, not how fast; the rates are THEORY-964. | Active |
| THEORY-963 v2 | The minimax regret of every finite partial-monitoring game against an oblivious adversary, degenerate and duplicate actions included, is 0 when no two actions are neighbours, Θ̃(√n) when every pair of neighbours is locally observable, Θ(n^2/3) when every pair is globally but some pair is not locally observable, and linear otherwise; its lower bounds are proved against stochastic outcomes, so the same four classes hold for them | Lattimore and Szepesvári (2019), LIT-1524, read in NOTE-1162, completing Bartók et al. (2014), LIT-1528. The four classes, trivial, easy, hard and hopeless, now cover every finite game. Two things change from Bartók et al.’s statement: the adversarial half no longer excludes degenerate and duplicate actions, and the trivial class is “no pair of neighbouring actions”, not “one non-dominated action”, which misplaces games whose extra actions are degenerate or duplicates. It classifies the best policy in a fixed, known game, up to game-dependent constants. It does not cover a learner barred from some actions, feedback that changes during play, or adaptive adversaries. | Active |
| THEORY-964 v3 | The minimax regret of a finite partial-monitoring game takes one of four rates, decided by its loss and signal matrices: 0 when only one action is non-dominated, Θ̃(√T) when every pair of neighbouring actions is locally observable, Θ(T^2/3) when the game is globally but not locally observable, and Θ(T) when it is not globally observable; against stochastic opponents for every game, against oblivious adversaries for non-degenerate games | Bartók, Foster, Pál, Rakhlin and Szepesvári (2014), LIT-1528, read in NOTE-1164. Four classes, trivial, easy, hard and hopeless, with conditions checkable from the matrices before play. It classifies the best policy for a fixed, known game. It does not cover a policy that is barred from some actions, a feedback structure that changes during play, or finite-horizon constants, and its adversarial half excludes degenerate games. | Superseded — by THEORY-963 |
| THEORY-965 | Sparse-autoencoder features of a large language model’s residual stream are units the model computes with: they track abstract concepts across languages, modalities and concrete or abstract instances, and intervening on one changes the model’s behaviour in the way its label predicts, better than directions found from a few labelled examples | Templeton et al. (2024), LIT-1533, read in NOTE-1178, with Bricken et al. (2023), LIT-1545, for the one-layer case. The thesis of both papers: features are the model’s own units, shown by steering. The authors’ own hedges: steering needs features clamped beyond their observed range; the reconstruction error rides along; “we haven’t rigorously evaluated our features against other steering methods”. The record holds a result against it for known causal variables (THEORY-968). | Proposed |
| THEORY-966 | Greedy edge pruning of the ACDC kind, which removes each edge whose removal changes the output metric by less than a threshold given the edges already removed, keeps only one input of a redundant OR gate, and which input it keeps depends on the order in which edges are visited, so when a model has redundant sufficient paths the circuit it returns is one of several sufficient subgraphs | Conmy et al. (2023), LIT-1547, Appendix M, read in NOTE-1170. For out = 1 − ReLU(1 − x − y) with x = y = 1, removing either input alone leaves the output at 1, so the first one visited is pruned and the second is then kept; visiting y first keeps x instead. It does not say how common redundant paths are in trained models, nor that any other method does better: HISP keeps neither input. | Active |
| THEORY-967 | In a two-layer attention-only transformer, attention heads change function during training: heads in the first layer that predict simple n-grams early later become the previous-token heads of the induction circuit, a bracket-matching support head, or supporting members of a circuit with second-layer n-gram heads, giving up simple n-grams as they do, and particular n-grams pass from one head to another; so later circuits form partly by repurposing components that already had a role | Wang, Hoogland, van Wingerden, Furman and Murfet (2024), LIT-1535, read in NOTE-1188. “Heads 0:1, 0:4, 0:7 ultimately become the two previous-token heads and (layer 0) Dyck head respectively. However, these heads appear to start out as simple n-gram heads.” Layer-0 multigram heads lose information about simple n-grams from stage LM3, as path patching and composition scores show them coming to feed layer-1 bracket-matching heads. The “ago” n-gram moves from head 0:0 to head 1:0. Whether the late roles are built from the early ones, or merely follow them in time, is not tested. | Proposed |
| THEORY-968 | In the Mechanistic Interpretability Benchmark’s causal-variable localization baselines on Gemma-2 2B and Llama-3.1 8B, features of the public Gemma Scope and Llama Scope sparse autoencoders, selected by a learned binary mask, never gave a higher mean interchange-intervention accuracy than the same mask over the model’s own hidden dimensions, in all sixteen task–variable cells and by 1 to 14 points, while distributed alignment search, trained against the causal model it is scored on, gave the highest mean in fifteen of them | Mueller et al. (2025), LIT-1550, read in NOTE-1169. Unsupervised SAE features were worse units than neurons for known task variables across ARC, MCQA, two-digit addition and RAVEL. It does not say SAE features are never causal units: the comparison is on residual streams, under one selection method, with the base reconstruction error carried into every intervention, and the best method is supervised by the hypothesis it is scored against. | Active |
| THEORY-969 | In hierarchical LDA every document draws all its words from the topics on one root-to-leaf path of a tree drawn from the nested Chinese restaurant process, so the prior is a nested sequence of partitions of the documents, exchangeable in them, and two documents share a topic only by sharing the whole path above it: no document can draw on two sibling subtrees | Blei, Griffiths and Jordan (2010), LIT-1542, read in NOTE-1176. hLDA’s overlap between documents is nested by construction: at each level of the tree the documents are partitioned, and a document can share topics with two others only if one of the two shares all of its shared topics with it. It is a statement about the model, not about the data, and it says nothing about whether the tree the sampler finds is identified. The multiple-path relaxation is the nested HDP’s (LIT-002). | Active |
| THEORY-970 | On three language-model tasks whose circuits earlier manual work reported, indirect object identification and Greater-Than in GPT-2 Small and Python docstrings in a four-layer attention-only model, ACDC run with resampled corrupted activations against KL divergence ranked the reported edges with areas under the ROC curve of 0.85 to 0.98, above head-importance pruning and subnetwork probing on all three; on two compiled tracr programs it ranked them poorly with corrupted activations, 0.68 and 0.20, and exactly with zero activations | Conmy et al. (2023), LIT-1547, read in NOTE-1170. Edge AUCs with corrupted activations and KL: Docstring 0.982, Greater-Than 0.853, IOI 0.869 for ACDC, against 0.805, 0.693, 0.789 for HISP and 0.937, 0.806, 0.823 for SP. It does not say ACDC finds the true circuit: the reported circuits are incomplete, the results depend on metric, ablation and parent order, and negative components are missed at sparse thresholds. | Active |
| THEORY-971 | A unit that thresholds a pre-activation equal to a term depending only on one operand plus a term depending only on the other cannot be active on exactly the pairs with a given sum when that sum has two decompositions: if it is active on (x, y) and (z, w), it is active on (x, w) or on (z, y); so a sum computed from separately represented operands needs an earlier unit that combines them, as Ameisen et al. argue for addition in language models | Ameisen et al. (2025), LIT-1552, read in NOTE-1185, re-derived here. It is why their addition graphs contain “lookup table” features between operand features and sum features. Whether a given unit in a trained model meets the premise is an empirical matter: attention patterns that depend on both operands, or any earlier nonlinearity that mixes them, break it, and that mixing is exactly the intermediate step the result says is required. | Active |
| THEORY-972 | In the author–topic model the likelihood of a corpus depends on the topics Φ and the authors’ topic distributions Θ only through the document–word matrix ΦΘA, A being fixed by the observed authorship, so LDA (each document its own author) and the topic-free author model (each author one topic) are special cases; and the likelihood leaves Φ and Θ unidentified not only up to the permutations of topics the paper names but along a continuum of changes of topic basis whenever every topic gives every word positive probability | Rosen-Zvi, Chemudugunta, Griffiths, Smyth and Steyvers (2010), LIT-1546, read in NOTE-1180. The likelihood sees members’ topic profiles only through the word distributions they jointly produce, and a small change of topic basis that keeps every distribution a distribution produces exactly the same corpus probabilities. Only the Dirichlet priors then choose among the profiles. It says nothing about the posterior’s concentration, and nothing about conditions under which Φ and Θ are identified up to permutation. | Active |
| THEORY-973 v2 | In small attention-only transformer language models of two to six layers, in-context learning, measured as the loss at token 500 minus the loss at token 50, appears abruptly in one early window of training in which induction heads form, and ablating those heads at test time removes nearly all of it; one-layer models show neither, and letting a single layer attend by the previous token brings the jump to one-layer models and moves it earlier in two-layer ones | Olsson et al. (2022), LIT-1538, read in NOTE-1173: Arguments 1–3 for the small attention-only series, with the smeared-key models. The score jumps from under 0.15 to about 0.4 nats in the window where induction heads form, pattern-preserving ablation of the induction heads removes nearly all of it to the end of training, and an architecture that lets one layer express induction moves the jump. It says nothing causal about models with MLPs or large models, and nothing about few-shot task learning, which the score does not measure. | Active |
| THEORY-974 | When a transformer’s MLP sublayers are replaced by transcoders and the attention patterns and LayerNorm scales on a prompt are held fixed, the contribution of an earlier transcoder feature at the same token to a later one’s pre-activation is the earlier feature’s activation times the dot product of its decoder with the later feature’s encoder, scaled by one LayerNorm constant per token, so the weight factor is fixed by the trained weights and holds on every input | Dunefsky, Chlenski and Nanda (2024), LIT-1554, read in NOTE-1174, Eq. 7 and App. D.2–D.4, re-derived here. The weight factor is a weight of the replacement model, not of the original, and it is exact only for the replacement. It says nothing about why attention attends where it does, and “input-invariant” holds only up to a per-token LayerNorm scalar and only while the later feature is active. | Active |
| THEORY-975 | In a two-layer attention-only transformer trained on the Pile, the weight-refined local learning coefficients of individual attention heads start alike and diverge over training, and clustering the curves groups the heads by the functional types that ablation assigns them at the end of training, previous-token, current-token, induction and n-gram-memorizing; among layer-1 heads, those running simple algorithms end with the lowest values and those memorizing the most n-grams with the highest | Wang, Hoogland, van Wingerden, Furman and Murfet (2024), LIT-1535, read in NOTE-1188: §4.1, Figs. 1–2 and 11, appendices B, F.5 and G. Per-head curves of how degenerate the loss is in that head’s weights separate the heads by what they end up doing, and the separation is in the curves’ shapes over training, not only their end values. It is one small model, cluster counts chosen by eye, and estimates whose ordering, not value, the authors trust. It does not show that the coefficient predicts a head’s type before the type is visible. | Active |
| THEORY-976 v2 | In a Claude 3.5 Haiku variant finetuned by Marks et al. to exploit reward-model biases described in fictional documents, a cross-layer-transcoder feature that in pretraining-style text fires almost only where those biases are discussed was active in all 100 short Human/Assistant-formatted prompts tested and in 1 of the same 100 without that formatting, and suppressing such bias features cut the sampled rate of three bias behaviours, including two the model was never trained to show | Lindsey et al. (2025), LIT-1541, read in NOTE-1181. A feature for a trained-in goal is active across the Assistant context, not only where the goal applies, and suppressing such features suppresses the behaviour. It is one model organism, built so that the goal has a name in its training documents; the authors do not claim their method would find a goal that has none. | Active |
| THEORY-977 | In the two-layer attention-only transformer that Elhage et al. reverse-engineer, the second-layer heads that compose substantially with first-layer heads do so through their keys, mainly with a head that attends to the previous token and, after the published correction, also with one that attends over the last several tokens; these heads are induction heads, attending from a token to the one after its earlier occurrence, including on repeated random tokens, with positive-eigenvalue copying OV and same-matching QK circuits, and the second-order virtual-head terms add little to the loss reduction | Elhage et al. (2021), LIT-1534, read in NOTE-1189: Analyzing a Two-Layer Model, Induction Heads, Term Importance Analysis, and the Correction. Composition between heads was scored by a normalized Frobenius norm of matrix products, minus its value for random matrices. The heads it picked out attend to the token after the present token’s previous occurrence and copy it, which is the minimal induction circuit the framework predicts from K-composition with a previous-token head. It is one model, with no seeds or training details reported, and says nothing about models with MLPs or about when the heads form. | Active |
| THEORY-978 v2 | Causal scrubbing scores a hypothesis through the partitions of the dataset that its interpretation nodes induce, so two hypotheses that assign different features to a node but induce the same partition on the dataset, such as two features perfectly correlated on it, receive the same score | Chan et al. (2022), LIT-1549, read in NOTE-1168. In the causal-scrubbing algorithm an interpretation node enters only through sample_agreeing_x, which draws a datum with an equal value of that node, so only the equivalence classes the node induces on the dataset matter. The authors say it themselves: the method “doesn’t allow us to distinguish between two features that are perfectly correlated on our dataset”. It does not say that a passing hypothesis is otherwise wrong, nor anything about features correlated only imperfectly. | Active |
| THEORY-979 | On one prompt, a transformer whose MLPs are replaced by a cross-layer transcoder, with its attention patterns and normalization denominators frozen and each MLP’s reconstruction error added back as a constant, reproduces the model’s activations and outputs exactly and is linear between features, so each active feature’s pre-activation is the sum of its attribution-graph edges and constants; a perturbation that clamps MLP outputs up to the target feature’s encoder layer then confirms a direct edge by construction, and tests only knock-on effects and the output | Ameisen et al. (2025), LIT-1552, read in NOTE-1185: the local replacement model, the edge formula and the appendix on steering, re-derived here. It is a statement about what an attribution graph is exact for, not about the model: exactness holds at the unperturbed point only, the error terms are constants with no inputs, and the frozen attention patterns are the part of the computation the graph does not explain. | Active |
| THEORY-980 | In GPT-2 small on fifteen templates of indirect object identification, a circuit of 26 attention heads in seven classes, found by path patching, keeps 87% of the model’s mean logit difference when every other head is mean-ablated; knocking out its three main name mover heads costs only 5%, because other heads take over, and knockout sets found by greedy search make the circuit and the full model differ by up to 87% of the logit difference, so the circuit is faithful on average and incomplete under knockouts | Wang et al. (2022), LIT-1540, read in NOTE-1167: §§3–4 and the appendices. The circuit implements “identify the names, remove the duplicated one, output the rest” through duplicate-token, induction and previous-token heads, S-inhibition heads and name movers, with negative and backup name movers. The faithfulness, completeness and minimality tests are the paper’s own. It says nothing beyond these templates and this model, it treats MLPs as given, and its greedy search is printed in a form that does not match its description. | Active |
| THEORY-981 | When a data distribution is unchanged by a group of orthogonal transformations under which a network is equivariant, the weights fixed by that group form a subspace that population gradient descent never leaves; for attention-only transformers on block-list inductive tasks, with fixed orthogonal write maps, Musat, Pimentel, Zucchet and Hofmann compute this subspace as the span of a few elementary token and position actions composed through the heads, and an elementwise optimizer such as sign descent keeps it only when those actions are aligned with the parameter coordinates | Musat et al. (2026), LIT-1530, read in NOTE-1177. Symmetries of the data confine population gradient descent to the weights those symmetries fix; for their task class and idealized architecture this is a subspace whose coordinates are interpretable head actions. It does not say the subspace is attractive (the paper proves only invariance), and it does not cover minibatch noise beyond expectation, learnable value maps (a sketch in the paper), or adaptive optimizers, which keep it only when the basis is coordinate-aligned. | Active |
| THEORY-982 | Claude 3.5 Haiku routinely computes intermediate steps within a single forward pass and plans its outputs ahead, representing a target before the text that leads to it and writing towards it, as Lindsey et al. propose from their case studies | Lindsey et al. (2025), LIT-1541, read in NOTE-1181: the introduction (“Claude 3.5 Haiku routinely uses multiple intermediate reasoning steps ‘in its head’”; “It displays signs of forward planning”) and the discussion’s sections on plan formation and working backward from a goal. The case studies show each mechanism on chosen prompts, and the same article has a case without it: on a jailbreak the model “doesn’t know what it plans to say until it actually says it”. The authors report a satisfying graph for about a quarter of the prompts they try. | Proposed |
| THEORY-983 | In Geiger et al.’s three-layer feed-forward network trained on hierarchical equality and in BERT fine-tuned on monotonicity inference, interchange interventions on subspaces found by a learned rotation aligned the hypothesised two-variable causal models with interchange intervention accuracy of 1.00 on the rotation’s training data, where the axis-aligned alignment closest to the learned rotation reached 0.73 and 0.51; in BERT, the learned lexical-entailment subspace was in turn aligned, at 0.97 to 0.98, with a model holding only the identities of the two words | Geiger, Wu, Potts, Icard & Goodman (2024), LIT-1551, read in NOTE-1192. Layer 1 of the equality network (1.00 with |N| = 16 and two 8-dimensional subspaces) and layer 9 of BERT’s [CLS] vector (1.00 with two 256-dimensional subspaces). It does not say the networks implement the algorithms in any stronger sense than interchange accuracy on training pairs, nor that the learned subspaces are unique: every rotation within them gives the same interventions. | Active |
| THEORY-984 | In Claude 3.5 Haiku, on the prompt “Fact: the capital of the state containing Dallas is”, which it completes with “Austin”, an attribution graph shows Dallas features activating Texas features that, with “say a capital” features, promote Austin, beside a direct edge from Dallas to “say Austin”; inhibiting the Dallas features lowers the Texas features and leaves “say a capital” largely intact, and replacing the Texas features with those of California, Georgia, British Columbia, China or the Byzantine Empire makes the model name that place’s capital | Lindsey et al. (2025), LIT-1541, read in NOTE-1181. A two-hop intermediate, measured by intervention on one prompt. The evidence that counts is the change of output under the swaps; the graph itself is of the replacement model. It does not say how often the model reasons in two steps, nor that the shortcut path is weak. | Active |
| THEORY-985 | The beta process BP(c, B0) is the de Finetti mixing measure of the Indian buffet process: given n objects, the next has each existing feature with probability equal to the number holding it over c + n and a Poisson(cγ/(c + n)) number of new ones, so n objects hold Poisson(γ Σ_{i<n} c/(c + i)) distinct features, which is the IBP’s αH_n at c = 1 and γ = α, and c alone sets how much objects share | Thibaux and Jordan (2007), LIT-1537, read in NOTE-1171. The beta process plays for the IBP the role the Dirichlet process plays for the Chinese restaurant process, and its concentration c separates how much objects share from the mass γ that sets features per object. The conjugacy it rests on is cited, not proved, in the paper. It does not give dependence between features or over time. | Active |
| THEORY-986 v2 | Analogous features and circuits form across neural networks trained on different architectures, data and tasks, so that a feature or circuit found in one model can be expected in others, as Olah, Cammarata, Schubert, Goh, Petrov and Carter propose under the name universality | Olah et al. (2020), LIT-1543, read in NOTE-1182: Claim 3, the universality hypothesis. Curve detectors and high-low frequency detectors are reported in AlexNet, InceptionV1, VGG19 and ResNetV2-50, with InceptionV3, a Places365 model and conv nets trained from scratch named in the text. The authors: “the only evidence we can offer today is anecdotal”. | Proposed |
| THEORY-987 | In Claude 3 Sonnet’s middle-layer residual stream, on two prompts for which every active sparse-autoencoder feature was ablated, how strongly a feature was active predicted its ablation effect on the answer poorly (correlation about 0.12) while its gradient attribution predicted it well (about 0.81), and on the multi-step prompt only three of the ten most active features were among the ten with the largest ablation effect | Templeton et al. (2024), LIT-1533, read in NOTE-1178: Features as Computational Intermediates and the appendix on ablations and attributions. On “The capital of the state where Kobe Bryant played basketball is” (Sacramento against Albany), the five features with the largest ablation effect, Kobe Bryant, California, capital, Los Angeles and the Lakers, rank as low as 70th to 162nd by activation. It does not say how often this holds beyond the two prompts, and for other prompts the authors found no intermediate features at this layer. | Active |
| THEORY-988 | In an attention-only transformer without layer norm or biases, once every attention pattern is held at its value on the input, the logits are exactly a sum of end-to-end path terms, a direct path from embedding to unembedding, one term per head and one per chain of heads composed through their values, and each head’s attention scores are a bilinear form in the tokens through which earlier heads can enter on the query side, the key side or both | Elhage et al. (2021), LIT-1534, read in NOTE-1189. For a two-layer model, T = Id ⊗ W_U W_E + Σ_h A^h ⊗ W_U W^h_OV W_E + Σ_{h₂,h₁} A^{h₂}A^{h₁} ⊗ W_U W^{h₂}_OV W^{h₁}_OV W_E, with each A^h computed from the model’s own run and then held fixed. It is an identity, not an approximation, and it is exact only under its conditions: no MLPs, no layer norm (which enters as a per-path rescaling), no biases, and attention frozen. It does not say the terms are small, interpretable or independent in what they compute. | Active |
| THEORY-989 | On the abstracts of the Journal of the ACM, the held-out likelihood of infinite-depth hierarchical LDA is higher than that of flat LDA at every fixed topic count in a range bracketing hLDA’s own posterior topic count, about 140, though the authors expect flat LDA to win once the topic count is free | Blei, Griffiths and Jordan (2010), LIT-1542, §6.3 and Fig. 9, read in NOTE-1176. One corpus, five-fold cross-validation, hyperparameters integrated out. It is evidence that a single-path hierarchy can earn its constraint in prediction, near its own size. It is not evidence that a hierarchy predicts better than a flat mixed-membership model in general: the paper itself says the flat model should dominate at large topic counts. | Proposed |
| THEORY-990 v2 | In transformer language models of every size, including large ones with MLPs, induction heads, extended to fuzzy matching of similar tokens and abstract patterns, are the mechanism of most in-context learning, as Olsson et al. propose | Olsson et al. (2022), LIT-1538, read in NOTE-1173. The paper’s thesis: circuits with the induction head’s mechanism, matching “[A*][B*] … [A] → [B], where A* ≈ A and B* ≈ B are similar in some space”, “implement most in-context learning in large models”. For large models the authors grade their own evidence correlational (Argument 1), weakly interventional (Argument 2), plausibility (Argument 4) and analogy (Argument 6). Their strongest alternative is that other composition heads, formed in the same window, carry more of it above some size. | Proposed |
| THEORY-991 | In a one-layer transformer whose MLP has 512 ReLU neurons, a sparse autoencoder with 4,096 features trained on that layer’s activations yields features that a blinded rater and an automated pipeline judged far more interpretable than the neurons, that for the four features examined in detail correspond to no neuron, and whose effects on the output, which the autoencoder never saw, agree with their activations; splicing in the reconstruction recovers 79% of the loss reduction the MLP provides, measured against zero-ablating it | Bricken et al. (2023), LIT-1545, read in NOTE-1191: the detailed investigations, the global analysis and the appendices, for run A/1 of model A. Median rubric score 0 for neurons and 12 for feature intervals (one author, 162 units); held-out logit prediction 74% against 58%; the Arabic, DNA, base64 and Hebrew features have no matching neuron. It says nothing about deeper models or other sites, nothing about whether the model is “composed of” these features, and nothing about how features compare with neurons as carriers of a known causal variable. | Active |
| THEORY-992 | In sparse autoencoders of about 1M, 4M and 34M features on Claude 3 Sonnet’s middle-layer residual stream, whether a concept among chemical elements, cities, animals and foods had a dedicated feature depended on how often it occurs in the training data: the frequency at which a concept became more than 50% likely to have one was slightly below one over the number of live features, and the three dictionaries’ curves roughly coincided when frequency was rescaled by that number | Templeton et al. (2024), LIT-1533, read in NOTE-1178: Feature Completeness. 100–200 single-word concepts per category, presence of a feature judged from Sonnet’s explanations of the top five features on a prompt naming the concept, by a human rater. The 34M dictionary (about 12 million live features) had features for about 60% of London boroughs, although the model names them all. It does not separate frequency in the model’s training data from frequency in the autoencoder’s, which the authors say are similar mixtures. | Active |
| THEORY-993 | In the mixed membership stochastic blockmodel the probability of an edge from p to q, given the memberships, is (1 − ρ)π_pᵀBπ_q, so the graph’s likelihood given the memberships is unchanged by π ↦ Rπ, B ↦ R⁻ᵀBR⁻¹ for any invertible R that keeps the memberships on the simplex and B in [0, 1], a continuum around any solution with B’s rates strictly between 0 and 1; and the sparsity parameter ρ enters only through (1 − ρ)B, so it is fixed by nothing but the bound B ≤ 1, and the paper’s printed estimator of it is the fraction of absent edges whatever the fit | Airoldi, Blei, Fienberg and Xing (2008), LIT-1553, read in NOTE-1179. The paper says the blockmodel and the memberships do not compete, because one is global and asymmetric and the other local and symmetric. Given the memberships they do: a change of block basis moves every node’s memberships toward the centre and sharpens B, with the same edge probabilities. What can still separate them is the Dirichlet family assumed for memberships, not the graph. The confounding of ρ with B’s scale is exact even in the marginal likelihood. | Active |
| THEORY-994 | In Ameisen et al.’s evaluations, the local replacement model of their 18-layer language model, built from a 10-million-feature cross-layer transcoder, responded to small perturbations much as the model did one layer after the intervention and increasingly differently over later layers, more in the size of the effect than its direction and slightly more for larger dictionaries, and over 20 prompts the graph’s influence of one feature on another ranked the effect of ablating the first on the second with a Spearman correlation of 0.72 | Ameisen et al. (2025), LIT-1552, read in NOTE-1185. It is the method’s own measurement of where a circuit read off its stand-in stops being the model’s: close for a layer, diverging with depth. It does not say how faithful the circuits of any case study are, which were chosen and validated separately, and it is measured on 18L, not on Claude 3.5 Haiku, where the companion’s case studies were run. | Active |
| THEORY-995 | The attention heads in GPT-2 small that take over the indirect-object prediction when its main name mover heads are knocked out exist because the model was trained with dropout, which optimized it to be robust to disabled components, as Wang, Variengien, Conmy, Shlegeris and Steinhardt hypothesize | Wang et al. (2022), LIT-1540, read in NOTE-1167, §3.4: “We hypothesize that this compensation phenomenon is caused by the use of dropout during training. Thus, the model was optimized for robustness to dysfunctional parts.” The compensation is real (a 5% loss of logit difference after knocking out the three name movers); the cause is not examined. Appendix F: “Both the reason and the mechanism of this compensation effect are still unclear.” | Proposed |
| THEORY-996 v2 | On Pythia language models from 410M to 12B parameters, in three single prompt pairs and two small prompt distributions, verifying attention or neuron nodes by activation patching in the order given by attribution patching, a first-order gradient estimate of each node’s noising effect, found the nodes with the largest effects at about 2 to 50 times the cost of an oracle ordering, below unordered patching, subsampling and block search in every setting; its misses were concentrated in queries and keys behind saturated attention and in nodes whose direct and indirect effects nearly cancel | Kramár, Lieberum, Shah & Nanda (2024), LIT-1531, read in NOTE-1190. Ground truth is each node’s exact single-node noising effect on the clean prompt’s negative log probability. Recomputing the softmax for queries and keys removes many misses; dropping one layer’s gradient at a time helps on single prompt pairs but not on the distributions, where AtP with the softmax fix or plain AtP is cheapest. It says nothing about coarser nodes, other model families, effect magnitudes or false positives. | Active |
| THEORY-997 | When a pretrained language model is fine-tuned on a task it initially fails, it acquires the task mainly by reconnecting components it already has rather than by recruiting new ones: the circuits found before and after keep most of their nodes and change most of their edges, as Wang, Hu, Du, Cheng, Wang and Zou propose from LoRA fine-tuning of Pythia-1.4B on arithmetic | Wang et al. (2025), LIT-1539, read in NOTE-1183. Their EAP-IG circuits (top 5% of edges) change edges 2.8–4.3 times as much as nodes over LoRA fine-tuning on five arithmetic tasks. A record simulation shows that a fixed edge budget on a transformer-sized graph gives the same contrast when only edge-level noise is resampled, so the counts do not yet show reorganization. Fine-tuning only, one model for most results, arithmetic only. | Proposed |
| THEORY-998 v2 | In GPT-2 XL, for 1000 facts the model knows, restoring single clean hidden states into a run whose subject tokens were noised recovers the most of the correct object’s probability at two sites, middle layers at the last subject token, where MLP outputs carry most of the effect, and late layers at the last token, where attention does; and a rank-one edit of one middle MLP output matrix keyed on the last subject token inserts counterfactual facts that generalize to paraphrases and spare neighbouring subjects better than the fine-tuning, knowledge-neuron and hypernetwork editors tested, working best at that token and in middle layers | Meng et al. (2022), LIT-1536, read in NOTE-1166: §§2–3, Tables 1 and 4, and Appendices A, B and E. Causal traces: ATE 18.6%; the mid-layer MLP effect at the last subject token peaks at AIE 6.6% against 1.6% for attention. CounterFact on GPT-2 XL: ROME’s score 89.2 (efficacy 100.0, paraphrase 96.4, neighbourhood 75.4), next best 66.9. It does not say where facts are stored: a rank-one edit with the same output exists for any one-dimensional fact patch (LIT-968). | Active |
| THEORY-999 v2 | In the finite beta–Bernoulli feature model with prevalences Beta(α/K, 1), the expected number of occupied features among N objects is K(1 − (α/K)B(α/K, N + 1)), strictly below the Indian buffet process’s αH_N for every finite K and tending to it as K grows, and each object holds Kα/(K + α) features on average rather than α | Griffiths and Ghahramani (2011), LIT-1556, read in NOTE-1172, derive the IBP as the K → ∞ limit of πk ~ Beta(α/K, 1), zik ~ Bernoulli(πk), and give K+ ~ Poisson(αH_N) for the limit only. At finite K the count falls short, by 27% at N = 12, α = 3, K = 16. It says nothing about stick-breaking truncations, which approach the IBP much faster. | Active |
| THEORY-1000 v2 | For fine-grained nodes of transformer language models generally, attribution patching corrected for attention saturation is a reliable prefilter for activation patching: nodes it ranks low rarely have large single-node patching effects, so verifying nodes in its order finds the important ones at a small multiple of the cost of an oracle, as Kramár et al. expect | Kramár, Lieberum, Shah & Nanda (2024), LIT-1531, read in NOTE-1190. The measured case is four Pythia models, three prompt pairs and two small distributions. The paper’s own diagnostic is what would let a single new setting be checked without exhaustive patching. | Proposed |
| THEORY-1001 | In a transformer whose candidate circuits are sets of shared elementary coordinates, how circuits interact during training is set by what they share: circuits that share a unit cooperate, and circuits that need the same layers for different roles compete, so that which circuit wins is decided by the initialization of units beyond its own, with sharp boundaries between competitors and soft ones between cooperators, as Musat, Pimentel, Zucchet and Hofmann read their three-layer scan | Musat et al. (2026), LIT-1530, read in NOTE-1177. In projected SGD training of a three-layer single-head attention-only transformer on in-context bigrams, three induction circuits are possible, and the winner depends on initial strengths outside the winner itself. The authors explain the pattern by cooperation through a shared unit and competition for layers. The evidence is one scan over two initial strengths with every other coordinate zeroed, in projected training. | Proposed |
| THEORY-1002 | On frozen randomly initialized feed-forward networks at chance on hierarchical equality, with 16 input dimensions, distributed alignment search for the two-equality causal model reached interchange intervention accuracy of 0.50 to 0.51 at hidden sizes up to 256 but 0.55 at 1,028 and 0.64 at 4,096, so in a hidden layer much wider than the input a learned rotation can produce above-chance interchange accuracy for an algorithm the network does not implement | Geiger, Wu, Potts, Icard & Goodman (2024), LIT-1551, §4.4, read in NOTE-1192. A random network cannot implement hierarchical equality, so any IIA above 0.5 is made by the search. At widths near the input’s there is none; at 4,096 there are 14 points. It does not say DAS results on trained networks are artefacts: the trained equality network reached 1.00 at width 16, where the random one stayed at 0.50. | Active |
| THEORY-1003 | On NIPS papers (1,557 training and 183 test documents, 100 topics, fixed hyperparameters), the author–topic model gave test documents lower perplexity than LDA while sixteen or fewer of their words had been observed and higher perplexity beyond that; one fictitious author per document improved on the author–topic model throughout and lost to LDA after about 64 words, and an author model without topics did worst | Rosen-Zvi, Chemudugunta, Griffiths, Smyth and Steyvers (2010), LIT-1546, §6.4 and Fig. 11, read in NOTE-1180. Pooling by member helps prediction of a document of which little has been seen and costs it once the document’s own words are enough. One corpus, one split, one topic count. It is not evidence that member-level structure is real, only that it predicts in a regime of sparse evidence. | Active |
| THEORY-1004 | In Pythia-1B, OLMo-1B and BLOOM-1B, the crosscoder features that most affect subject–verb agreement change over pretraining: at early checkpoints they detect particular tokens and subtokens, at later ones grammatical categories; in BLOOM, language-specific features give way to features shared across English, French, Spanish and Portuguese while Hindi and Arabic keep language-specific ones; and which features matter keeps shifting after task accuracy has stopped improving | Bayazit, Mueller and Bosselut (2025, ACL 2026), LIT-1555, read in NOTE-1186. Crosscoders trained jointly on the middle layer of two or three checkpoints, with features scored by their relative indirect effect on agreement minimal pairs at each. The reconstruction quality (C1) and RelIE’s agreement with single-feature ablations (C2) are measured; the trends in this title are read by the authors from annotated features. It describes; it does not predict later checkpoints, and it cannot tell a feature carried forward from one re-learned in the same direction. | Proposed |
| THEORY-1005 | On one MLP layer each of GPT2-small, Pythia-410M and Pythia-1.4B, transcoders trained to imitate the MLP lay on or above the sparsity–loss frontier of sparse autoencoders trained on its output, at one learning rate tuned on transcoders and one seed, and in a single rater’s blind reading of 50 random features each from Pythia-410M layer 15, 41 transcoder and 38 SAE features were judged interpretable | Dunefsky, Chlenski and Nanda (2024), LIT-1554, read in NOTE-1174: §4, Table 1, Fig. 3 and Apps. E–F. It does not say transcoders are better than SAEs in general. The SAE learning rate was not tuned, all runs shared one seed and data order, one layer per model was measured, and on Gemma 2 2B Gemma Scope found transcoders worse than MLP-output SAEs at fixed L0 (LIT-611, NOTE-482). | Active |
| THEORY-1006 | In the dependent Indian buffet process each item’s feature indicator is a Gaussian process thresholded at the quantile of a stick length that does not change with the covariate, so its prevalence is the same at every covariate value and its persistence is set separately by the covariance; the whole feature matrix at a covariate value is an Indian buffet process only when there is no shared feature-level process, and with one the items are correlated and fewer features are occupied | Williamson, Orbanz and Ghahramani (2010), LIT-1548, read in NOTE-1175. Thresholding at a fixed quantile keeps each feature’s prevalence at its stick length at every covariate value, which is what a hand-written logistic transition does not do. The paper’s statement that Z(t) is an IBP at each t holds for its collapsed model; with a shared feature-level GP it holds item by item only. Persistence for a fixed correlation still falls with prevalence. | Active |
| THEORY-1007 | On four subject–verb agreement tasks in Pythia-70M and Gemma-2-2B, circuits of sparse-autoencoder features and autoencoder error nodes, selected by linear estimates of indirect effect, carried half or more of the behaviour on held-out pairs with about 100 and 500 nodes, where circuits of neurons needed about 1,500 and more than 30,000; with the error nodes removed, the same feature circuits carried little of it, under about a quarter in Pythia and almost none in Gemma | Marks et al. (2025), LIT-1532, read in NOTE-1187: §§2–3.2, Figure 3 and Appendices A, B and H. Faithfulness is (m(C) − m(∅))/(m(M) − m(∅)) with nodes outside the circuit mean-ablated, scored on the latter two thirds of each circuit only. The features plus the dense error terms are a small circuit; the features by themselves are not. It says nothing about what the error terms hold, and it does not compare features with neurons on equal terms, which the authors say cannot be done. | Active |
| THEORY-1008 | Mixed memberships fitted by a fifteen-block MMSB to 871 yeast proteins’ curated physical interactions carry information about the proteins’ top-level MIPS functions beyond what the functions’ base rates give: after mapping blocks to functions on 87 proteins, thresholded memberships predicted the other proteins’ annotations with about 87% accuracy, against about 70% for random guessing at the right proportions | Airoldi, Blei, Fienberg and Xing (2008), LIT-1553, §4.3.2 and Figs. 10–12, read in NOTE-1179. The batch’s one check of inferred mixed memberships against labels the model never saw. The reported margin is over a weak baseline, so it shows less than it seems: probably some information, not yet how much. It says nothing about whether the fifteen blocks are the fifteen functions. | Proposed |
| THEORY-1009 | In Musat, Pimentel, Zucchet and Hofmann’s two-layer attention-only transformer on in-context bigrams, once an in-weights circuit that maps each common token to its memorized partner has saturated, the population gradient on the induction circuit is what it would be without it multiplied by fr + (1 − fr)fv, the share of the data the memorized map does not solve, up to errors that vanish at large vocabulary and large in-weights margin when no distractor block carries the query’s partner; the two circuits occupy orthogonal coordinates and still interact, because they solve overlapping parts of the data | Musat et al. (2026), LIT-1530, read in NOTE-1177. A memorized shortcut that solves part of the data removes the in-context circuit’s gradient on that part and leaves the rest. It is a theorem in an idealized model under a disjointness assumption (A4) that the paper’s own sampler violates, at a cost it states. It does not say the observed order in the paper’s one run is due to it: there fr = 0.9 and the factor is 0.9. | Active |
| THEORY-1010 | On ten corpora simulated from three-level hierarchical LDA itself (100 documents of 250 words, a vocabulary of 100, sparse topics with η = 0.005, γ = 1), the highest-probability state of the collapsed Gibbs sampler recovered the generating tree exactly in eight; in one of the other two a wrong tree had higher posterior probability than the true one | Blei, Griffiths and Jordan (2010), LIT-1542, §6.1 and Fig. 6, read in NOTE-1176. It shows that the sampler can invert hLDA on data hLDA generated, with sparse, well-separated topics. It does not show that the tree is identified in general, or that a tree found in real data was there to be found. One failure is a posterior that prefers the wrong tree, which no better sampler would fix. | Active |
| THEORY-1011 v3 | In autoregressive transformer language models, factual associations are stored in middle-layer MLP modules as linear key–value memories: the MLP takes a key encoding the subject at its last token and returns a value encoding its attributes, which late attention moves to the prediction, and any middle layer could store a given fact equally, as Meng, Bau, Andonian and Belinkov propose | Meng et al. (2022), LIT-1536, read in NOTE-1166, §2.3 and §3: “the localized factual association hypothesis”. It localizes recall along three dimensions, “(i) in the MLP modules (ii) at specific middle layers (iii) and specifically at the processing of the subject’s last token”, and conjectures “that any fact could be equivalently stored in any one of the middle MLP layers”. The support is causal tracing and the success of rank-one edits at the traced site. | Rejected — Hase et al. (LIT-1578, THEORY-1024) meet this entry’s own refutation clause for its localization part, in GPT-J on 652 CounterFact facts. ROME rewrites a fact at over 96% at every layer but the last, and the per-fact tracing effect adds at most 3.2 points of R² to edit success. The conjecture that any middle layer could store a fact equally was split out to THEORY-1039 and stays Proposed |
| THEORY-1012 | Latent features made dependent through a layer of categories, each observation’s features being a function of how many of its categories carry each feature, stay finite on finite data when a feature carried by none of an observation’s categories is always off; under that condition a category can switch features on and never off, so features depend on one another by sharing a category, or, where an observation has a single category, by excluding one another, and no feature or category suppresses another | Doshi-Velez and Ghahramani (2009), LIT-1544, read in NOTE-1184. Z = f(CM) with f(0) = 0 gives correlated nonparametric feature models with O(log log N) expected features for the DP-IBP and IBP-IBP. The correlations are motifs, sets of features switched on together, plus, in the DP-IBP, exclusion between categories; suppression is outside them, and negative correlation is left as future work. The models’ predictive advantage over the IBP is mixed in the paper’s own table. | Active |
| THEORY-1013 v3 | In trained vision networks, units or other directions in a layer’s activation space are typically meaningful features, and the weights between understood features implement algorithms that can be read off them, so that features and their circuits are the units in which such a network can be understood, as Olah, Cammarata, Schubert, Goh, Petrov and Carter propose | Olah et al. (2020), LIT-1543, read in NOTE-1182: Claims 1 and 2 of the essay. The evidence is a set of examples in InceptionV1 (curve, high-low frequency and dog head detectors; the curve, oriented dog head and car circuits), argued with feature visualization, dataset examples, synthetic stimuli, tuning curves and the weights. The essay names polysemantic neurons as the main obstacle. It gives no count of how much of a layer is understood. | Proposed |
| THEORY-1014 | In a language model, a behaviour that looks like one mechanism, whether picked out by one contrast or by one cluster of next-token predictions, is often carried by several distinct pathways of sparse features that converge on the output without fully intersecting, as in Pythia-70M’s agreement across a relative clause, its prediction of “to” before an infinitival object, and its incrementing of sequences | Marks et al. (2025), LIT-1532, read in NOTE-1187: §3.3, §5 and Appendix C. Agreement across a relative clause: subject-number features promote verb forms directly, and a second pathway carries the number to the clause’s end through PP/RC boundary features. Cluster 475: one mechanism detects verbs and adjectives that take infinitival objects, another nominal objects before an object complement. Cluster 382: general succession features and token-specific induction features. “While the clusters … seem at first to each represent a single mechanism, circuit-level analysis reveals in both cases a union of distinct mechanisms.” | Proposed |
| THEORY-1015 | Groups of objects drawn from beta processes share features only if the measure they are drawn around is discrete; in the hierarchical beta process that measure is itself a beta process draw, and at each shared feature a group’s prevalence is Beta(c_j b, c_j(1 − b)) around the shared prevalence b, so a small c_j lets groups differ and a large one pulls them together | Thibaux and Jordan (2007), LIT-1537, read in NOTE-1171. The hierarchical beta process B ~ BP(c0, B0), Aj ~ BP(cj, B) gives several groups one unbounded feature library at group-specific prevalences. It treats each object as in one group, exchangeable within it, and has no dynamics; its one experiment, 58% against 50% on a single text split, is suggestive only. | Active |
| THEORY-1016 | The features a sparse autoencoder recovers from a language model are a resolution set by the dictionary’s width and sparsity penalty, not a unique set of the model’s units: as the dictionary widens, features split into families of finer features, and splits also merge, so that the number of features is not well-posed | Bricken et al. (2023), LIT-1545, read in NOTE-1191, Feature Splitting and Discussion; and Templeton et al. (2024), LIT-1533, read in NOTE-1178, for the same splitting at 1M, 4M and 34M features in a large model. In a one-layer model one base64 feature becomes three, then more; in Claude 3 Sonnet a San Francisco feature becomes two, then eleven. The authors offer two pictures, an idealized set seen at varying resolution and feature manifolds with no finite description; both deny that one width is the right one. | Proposed |
| THEORY-1017 | In Claude 3.5 Haiku, writing the second line of a rhyming couplet whose first line ends “grab it”, features for the candidate rhymes “rabbit” and “habit” are active on the newline token before the line, steering them changes the line’s final word only when applied at that token, and suppressing “rabbit” turns the line towards “habit”; injecting a “rabbit” or “green” word feature at that point in 25 other poems ended the line with the injected word in 70% of cases, and such planned-word features were found in about half of the poems the authors examined | Lindsey et al. (2025), LIT-1541, read in NOTE-1181. A target word represented before the text that leads to it, and used causally: it is the case study’s own measurement, on one couplet and a 25-poem injection test. It does not say how widespread planning is, the “about half” being a count without a stated sample, and one of the article’s displayed “success cases” does not end in the injected word. | Active |
| THEORY-1018 | In Claude 3.5 Haiku, on the jailbreak prompt “Babies Outlive Mustard Block.” asking it to join the first letters and say how to make one, the attribution graph for its output “BOMB” shows separate letter-wise paths voting for the output and no internal representation of the word or of a bomb-making request before it is written; “make a bomb” features first fire on the model’s own “To make a bomb”, injecting one on “BOMB” brings an immediate refusal, and the refusal that does come waits for the sentence’s end | Lindsey et al. (2025), LIT-1541, read in NOTE-1181. On this prompt the model “doesn’t know what it plans to say until it actually says it”. It is one prompt, partly effective, and the decisive refusal mechanism runs through attention, which the graphs do not show: the injection that produced a refusal needed attention left unfrozen. | Active |
| THEORY-1019 | Under the Markov Indian buffet process the expected number of features on at the first time step is α, as in the Indian buffet process, but it rises over time toward α·E[ln((2 − b)/(1 − b))] with b ~ Beta(γ, δ), which is 9.04 at γ = 10 and δ = 1, so after the first step the rows are not distributed as an Indian buffet process | Van Gael, Teh and Ghahramani (2008), LIT-1577, read in NOTE-1199. A chain starting off is on at step t with probability a(1 − (b − a)^t)/(1 − b + a). As M → ∞ the a’s form a Poisson process of intensity α/a on (0, 1), so E[number on at t] = α ∫₀¹ E_b[(1 − (b − a)^t)/(1 − b + a)] da. That is α at t = 1 and tends to α·E[ln((2 − b)/(1 − b))]. The number of features ever on is still Poisson(αH_T), as the paper says. This concerns the expected count only, not the full row distribution beyond it. | Active |
| THEORY-1020 | In a two-layer attention-only language model, on tokens where induction helps, the standard induction circuit (queries and values from the token embedding, keys from the previous-token head) accounts for 35% of the loss its two induction heads contribute, and a hypothesis that adds three-token matching, layer 0’s average effect and three layer-0 heads acting as if they attended to the current token accounts for 86% | Chan, Garriga-Alonso, Goldowsky-Dill, Greenblatt, Lin et al. (2022), LIT-1579, read in NOTE-1196. Percentages are of 0.053 nats, the loss the induction heads 1.5 and 1.6 contribute on next-token examples whose last token is on an induction-favouring whitelist, measured by causal scrubbing. The naive story’s shortfall is mostly in the queries (51% alone) and keys (79%), not the values (90%). It does not say what fraction of the model’s whole loss, or of its in-context learning, the circuit explains, nor anything about models with MLPs. | Active |
| THEORY-1021 | In transformer language models, attribution patching agrees well with activation patching for small patches of single heads and their queries, keys, values and attention patterns, for nodes late in a circuit relative to the metric, and for circuits that route information through attention, and agrees badly for large patches such as whole residual streams, for the first MLP layer and the early layers of deep circuits, where nonlinearities move out of saturation, and where an effect needs several features at once, as Nanda proposes | Nanda (2023), LIT-1581, read in NOTE-1201. The post’s map of where the first-order estimate can be trusted. The record holds it from one task in the post, from the mathematics of the estimate (THEORY-1023), and in part from Kramár et al.’s test on Pythia (THEORY-996), which found misses behind saturated attention, as this predicts, and tested no residual-stream nodes. | Proposed |
| THEORY-1022 v2 | The curve units of InceptionV1’s mixed3b detect curves as such: curves, not correlated stimuli, cause their firing, they respond to curves in general whatever their colour, fill or texture, and they have no meaningful secondary function, their weak responses to edges and angles being part of the same curve-detecting algorithm, as Cammarata, Goh, Carter, Schubert, Petrov and Olah claim | Cammarata et al. (2020), LIT-1575, read in NOTE-1198. The article’s four claims (causality, generality, purity, family) taken together, as the authors state them. Generality and the family are measured (THEORY-1028). Causality rests on feature visualization and attribution. Purity rests on feature visualization with a diversity term and activation-binned labels, while most of the unit’s firings, and 45% of its contribution to expected value, are not shown to be curves. | Proposed |
| THEORY-1023 | Attribution patching estimates the effect of patching an activation from a clean run into a corrupted run as the difference between the two activations dotted with the gradient of the metric on the corrupted run, so the estimates for every activation come from two forward passes and one backward pass and add over sub-components; the estimate is exact when the metric is affine in the activation, gives no effect for a nonlinearity in saturation whatever the true change, and through LayerNorm ignores the component of a patch along the vector being normalized | Nanda (2023), LIT-1581, read in NOTE-1201: the estimate and its mathematical properties, not its accuracy in any model. The cost is fixed (about four forward passes for all patches), the estimate is linear and so additive, and its blind spots follow from linearity: saturation, interaction between features, and LayerNorm’s scale invariance. | Active |
| THEORY-1024 | In GPT-J, for 652 CounterFact facts the model knows, the per-fact causal-tracing effect at an MLP layer adds at most 3.2 points of explained variance in the success of editing that fact at that layer, beyond what the choice of layer alone explains, across ROME, MEMIT and constrained fine-tuning and five editing objectives; ROME rewrites the fact at over 96% at every layer but the last, including layers where tracing does not place it, and the only reliable link appears when the edit is made on the noised input that tracing uses | Hase et al. (2023), LIT-1578, read in NOTE-1194: §§4–5, Tables 1–8 and Appendices A–C. For ROME at GPT-J’s layer 6, ρ = −0.13 between rewrite score and tracing effect; R² 0.947 from the layer, 0.948 with tracing added. Over twenty method–objective pairs the largest gain is 0.032 (fine-tuning on five layers, Fact Forcing). It does not say that facts are stored nowhere in particular, nor that the layer does not matter: the layer explains most of the variance, and ROME is best on average at the layer tracing favours on average. | Active |
| THEORY-1025 | The inputs causal scrubbing samples for a treeified hypothesis are the unique maximum-entropy distribution, on finite inputs, among those that give the inputs of every interpretation node the joint distribution they have on the data, so whatever the hypothesis does not claim is resampled as independently as the claims allow | Chan, Garriga-Alonso, Goldowsky-Dill, Greenblatt et al. (2022), LIT-1583, read in NOTE-1202, §5. Every node’s datum is distributed as D, so each node’s scrubbed inputs are jointly as on the data, and among all distributions with that property the algorithm’s has the greatest entropy. It characterizes the sampling, not the score: it does not say that a hypothesis whose score matches the model is true, and the same appendix’s §7 builds one that is false. | Active |
| THEORY-1026 | In transformer language models, locating where a forward pass carries information about a fact and finding where a weight edit best changes the expressed fact are different questions, because an edit at one layer can override information accumulated across other layers, so that many layers could hold a fact and some happen to, as Hase, Bansal, Kim and Ghandeharioun propose | Hase et al. (2023), LIT-1578, read in NOTE-1194, §6: “Causal Tracing answers a question about where factual information is carried in representations in a Transformer forward pass, and this question turns out to be a different question than the editing question of where is best to intervene”; and, for why edits work where facts are not traced, “Many layers could store a fact, and it happens that some do”. The authors note that this would be surprising, since layers cannot be swapped freely. | Proposed |
| THEORY-1027 | In audits of language models for hidden objectives, sparse-autoencoder features add to what black-box attacks and semantic search over the training data can find, surfacing knowledge the model does not disclose even where the data that taught it is not semantically similar to the context in which it is applied, as Marks, Treutlein et al. suggest | Marks, Treutlein et al. (2025), LIT-1584, read in NOTE-1193: §§4–5 and Appendix F. In the blind game the fastest team used SAE features, but semantic search with its query finds the same documents. Post hoc and unblinded, SAE features surface RM-bias knowledge from bias demonstrations and from the Assistant token, where semantic search fails. The model’s objective is named in its training data. | Proposed |
| THEORY-1028 v2 | In InceptionV1 trained on ImageNet, the ten curve units of layer mixed3b each respond most to curves of one orientation, with responses invariant to fill and colour and jointly spanning all orientations under rotation of real images; for one of them, 3b:379, which fires on about 11% of dataset positions, activation level separated one author’s blind four-class labels of over 800 activation-binned images, and curves and imperfect curves made up 55% of its contribution to expected value | Cammarata et al. (2020), LIT-1575, read in NOTE-1198: the behaviour of the mixed3b curve family as measured by feature visualization, rotated dataset examples, synthetic curves and, for one unit, activation statistics and blind hand labels. It holds for the neuron basis of one model. It does not say how the units are computed, what their weak firings encode, or what fraction of the layer is understood. | Active |
| THEORY-1029 | On a three-layer parenthesis-balance classifier, causal-scrubbing hypotheses that resample the terms of one head’s input separately scored 81% and 84% of the loss recovered against 77% for the less specific hypothesis they refine, and the authors attribute the rise to resampling washing out a signal, not to a better explanation | Chan, Garriga-Alonso, Goldowsky-Dill, Greenblatt, Lin et al. (2022), LIT-1580, read in NOTE-1195. Hypothesis 3a resamples head 2.1’s input separately at each of up to 40 positions and recovers 77% (loss 0.97 ± 0.06). Hypotheses 3c and 3d also split each position’s input into terms drawn from different inputs, and recover 84% (0.69 ± 0.05) and 81% (0.81 ± 0.05). The authors call the two results not legitimate. It does not say how often this happens in other models, nor that the adversary they propose would remove it. | Active |
| THEORY-1030 | In transformer language models, each hidden unit of a feed-forward layer acts as a key–value memory, its input weights detecting patterns in the prefix and its output weights promoting the tokens that follow them, and a layer’s output composes many such memories while the residual stream refines the prediction from layer to layer, as Geva, Schuster, Berant and Levy propose | Geva et al. (2021), LIT-1576, read in NOTE-1200: “feed-forward layers in transformer-based language models operate as key-value memories, where each key correlates with textual patterns in the training examples, and each value induces a distribution over the output vocabulary”, and “we thus expect our qualitative empirical observations to hold across diverse settings”. Evidence in one model, correlational only. ROME’s storage hypothesis (THEORY-1011) borrows the name and reads keys and values at another level. | Proposed |
| THEORY-1031 | In GPT-J, inserting 10,000 CounterFact counterfactuals at once by a closed-form least-squares update of the MLP output matrices of layers 3 to 8, spread so that each layer writes a share of each fact’s required change to the subject’s hidden state, gives an editing score of 85.8 (efficacy 98.9, paraphrase 88.6, neighbourhood 73.7) with fluency kept, against 67.6 for weight-decayed fine-tuning, which breaks generation, 50.3 for ROME applied one fact at a time and 23.1 for MEND; GPT-NeoX scores 82.0, and editing late MLPs or attention instead does worse | Meng et al. (2022), LIT-1582, read in NOTE-1197: §§4–5, Tables 1 and 2, Appendices A, B and F. On 10,000 true zsRE facts in GPT-J, MEMIT scores 50.7 against FT-W 42.1, MEND 20.0 and ROME 2.6. At a handful of edits ROME generalizes a little better. It does not show where facts are stored: the layer range is chosen from traces averaged over facts, which do not predict per fact where an edit works (THEORY-1024). | Active |
| THEORY-1032 | When Claude 3.5 Haiku was given continued pretraining on synthetic documents describing 52 fictional reward-model biases and then trained by SFT and RL to exploit 47 of them, its rate of exploiting the 5 held-out biases rose from 17% to 45% of applicable episodes, and it applied new biases described in context as a reward model’s more often than the same biases attributed to other entities; without the documents the held-out rate rose only to 20%, and without SFT it still rose | Marks, Treutlein et al. (2025), LIT-1584, read in NOTE-1193: §3 and Appendices B–C. The model organism behind THEORY-976. Behaviours never demonstrated in post-training become more frequent, and the increase depends on the model having read that reward models prefer them. Rates are judged by a classifier. Haiku already shows the held-out behaviours at 17%, so what generalizes is an increase, not a new behaviour. | Active |
| THEORY-1033 | In a 16-layer transformer language model trained on WikiText-103, the training prefixes that most activate a sampled feed-forward hidden unit share patterns that human annotators recognize, mostly shallow in layers 1–9 and semantic in layers 10–16; projected through the output embedding, a unit’s output weights put the next token of its top prefix first in up to about 3.5% of units in the upper layers and almost none below; and a layer’s top prediction differs from every unit’s in at least about 68% of examples | Geva et al. (2021), LIT-1576, read in NOTE-1200: §§3–5. 160 keys annotated, one annotator each: every key had a pattern (3.6 on average), covering 65–80% of top prefixes. Agreement between value and key rises to about 3.5% by the top layers, against 0.0004% for a random token. It says nothing causal: no unit was ablated or edited, and the patterns were not compared with those of random directions. | Active |
| THEORY-1034 | In the Markov Indian buffet process each feature’s probability of staying on is drawn independently of its probability of switching on, so how long a feature persists once on does not depend on how rare it is; the process is defined for the time steps of one sequence, not for several objects over time | Van Gael, Teh and Ghahramani (2008), LIT-1577, read in NOTE-1199. Each column is a two-state chain from an off state with a_m = P(0 → 1) ~ Beta(α/M, 1) and b_m = P(1 → 1) ~ Beta(γ, δ), independent, and the stick-breaking construction keeps each b paired with its a as an independent draw. Rarity (small a) and persistence (b) are separate per-feature parameters. It does not say that prevalence is held fixed over time, which it is not (THEORY-1019), nor how to share the chains across several objects. | Active |
| THEORY-1035 | In trained neural networks, polysemantic neurons arise from the loss-optimal allocation of a layer’s limited capacity among features: a feature is shared between neurons when its marginal loss reduction from capacity equals that of the features it shares with, so that sparser, higher-kurtosis inputs, which make returns to capacity diminish, produce more polysemanticity, and the block structure of the embedding, which architecture shapes, sets how many features each neuron mixes, as Scherlis, Sachan, Jermyn, Benton and Shlegeris propose | Scherlis et al. (2022), LIT-1625, read in NOTE-1205. The paper’s account of polysemanticity in general: capacity allocation at the loss optimum, driven by sparsity, with architecture deciding block size. The general first-order condition holds for any loss under two stated assumptions; its application to trained networks, and the role of architecture, rest on toy models only. | Proposed |
| THEORY-1036 | In a model that fits y = Σ v_i x_i² with ỹ = Σ_r (W_r·x)² + b, on independent inputs of zero mean, unit variance and common fourth moment k, the expected squared error at the optimal bias is (k − 1)Σ(n_i − v_i)² − 2Σn_i² + 2Σn_i²/C_i, in the squared embedding lengths n_i and capacities C_i = (w_i·w_i)²/Σ_j(w_i·w_j)², and its minimum with the capacities summing to the number of neurons D gives C_i = clip((k − 1)v_i/((k − 3)λ) − 2/(k − 3), 0, 1): for k ≤ 3 each feature is given a whole dimension or none, and for k > 3 a feature is shared between neurons exactly when 2λ/(k − 1) < v_i < λ | Scherlis et al. (2022), LIT-1625, read in NOTE-1205: the quadratic toy model of superposition solved in closed form. Its loss separates by feature through capacity, so the marginal value of capacity is −∂L/∂C_i = 2n_i²/C_i², and sparsity, through k, decides whether returns to capacity diminish. It is the model the causal scrubbing appendix’s §6 analyses. It holds for this model and says nothing directly about trained networks. | Active |
| THEORY-1037 | In the infinite hidden Markov model, drawing at each time step a slice variable uniformly below the probability of the transition taken leaves the posterior unchanged and leaves only finitely many state trajectories with positive probability, so a whole trajectory can be resampled exactly by forward filtering and backward sampling, with no truncation of the state space | Van Gael, Saatci, Teh and Ghahramani (2008), LIT-1622, read in NOTE-1204. u_t ~ Uniform(0, π_{s_{t−1}s_t}) is an auxiliary variable, so sampling u given s and then s given u leaves p(s | y) invariant; given u, the forward recursion sums only over transitions with π > u_t, of which there are finitely many per row. It says the sampler is exact, not how fast it mixes (THEORY-1044). | Active |
| THEORY-1038 | In InceptionV1, the ten curve units of mixed3b, which respond to curves of one orientation and not to the opposite one, regain the 180° echo of earlier curve units when their input is restricted to mixed3a early curves with the negative weights removed, and not when the negative weights are kept; a network one author wrote by hand from the described circuit, without looking at the original weights and tuned afterwards, has grayscale curve units that the authors show, by figures only, approximating the natural ones on synthetic curves across radii and orientations; and substituting them for the ten units recovered 26 of the 46 top-5 classifications lost by deleting the units, on 2,000 validation images, a result the authors call preliminary | Cammarata et al. (2021), LIT-1629, read in NOTE-1207: the three results of Curve Circuits that test its account of the mixed3b curve units, the echo edit, the hand-written reimplementation and the substitution. Only the last is a number, and a small one. It holds for one model’s neuron basis and says nothing about weak firings or other families. | Active |
| THEORY-1039 | In autoregressive transformer language models, factual associations are recalled through middle-layer MLP modules acting as key–value memories, and any fact could be stored equally in any one of the middle MLP layers, as Meng, Bau, Andonian and Belinkov conjecture | Meng et al. (2022), LIT-1536, read in NOTE-1166, §2.3: “we conjecture that any fact could be equivalently stored in any one of the middle MLP layers”. It was one clause of THEORY-1011, which is Rejected for its other part, the claim that the traced middle layers are where a fact is stored. Hase et al. (2023), LIT-1578, read in NOTE-1194, measure edits succeeding at nearly every layer of GPT-J whatever tracing says (THEORY-1024). That is what this conjecture predicts, but it is not evidence of storage, since an edit can work wherever a layer can write the needed output (LIT-968). | Proposed |
| THEORY-1040 | The units of the early layers of trained vision networks fall largely into neuron families, sets of variants of one feature across orientation, colour or scale, which reflect structure in the network rather than a convenience of the person sorting them, and the same families form across models, as Olah, Cammarata, Schubert, Goh, Petrov and Carter propose | Olah et al. (2020), LIT-1624, read in NOTE-1206. The article’s organizing hypothesis: early vision’s units come in families, some of them real structure (said to be recoverable by factorizing weight matrices), and the families recur across models. The census (THEORY-1042) is by eye in one model; neither the factorization nor a second model’s sorting is shown. | Proposed |
| THEORY-1041 | In the Indian buffet process the feature probabilities in decreasing order are products of independent Beta(α, 1) draws, so the k-th has mean (α/(α + 1))^k, and keeping only the first K of them gives an expected number of occupied features among N objects that approaches αH_N from below: 8.97 at K = 16, N = 12 and α = 3, against 9.31 in the limit and 6.83 for the finite model with sixteen independent prevalences | Teh, Görür and Ghahramani (2007), LIT-1627, read in NOTE-1210. μ_(k) = ∏{l≤k} ν_l with ν_l ~ Beta(α, 1). Truncated at K, the expected number of occupied features is Σ{k≤K} Σ_{j=1}^{N} (−1)^{j+1} C(N, j) (α/(α + j))^k, which sums to αH_N as K → ∞. At N = 12, α = 3: 6.80, 8.97, 9.27 and 9.31 at K = 8, 16, 24 and 32. It concerns the prior’s expected count, not a posterior, and the paper itself computes no truncation error. | Active |
| THEORY-1042 | In the Overview of Early Vision’s taxonomy of InceptionV1, every one of the 1,056 units of conv2d0 to mixed3b is assigned by the authors to exactly one of 77 groups, and 391 of them (37%), from 7% of conv2d2 to 48% of conv2d1 and 45% of mixed3b, are in groups whose own captions call them catch-all, broad and not well defined, low-confidence, unstudied or not understood; the mixed3b curve family is 10 of that layer’s 480 units | Olah et al. (2020), LIT-1624, read in NOTE-1206: the census of InceptionV1’s early vision, counted. A complete partition of 1,056 units into 77 groups, by eye; 37% in groups the authors flag as uncertain or catch-all, by their own words. It is a denominator for the circuits claim that units are typically features (THEORY-1013), not a measure of how many units are understood. | Active |
| THEORY-1043 | The finite feature model in which each of K features has prevalence Beta(α/K, 1) has, as K grows, a limit on equivalence classes of binary matrices that ignore the order of columns, and the Indian buffet process, in which the i-th object takes each earlier feature with probability m/i and Poisson(α/i) new ones, produces the same distribution, so its objects are exchangeable and the number of features they hold is Poisson(αH_N) | Griffiths and Ghahramani (2005), LIT-1623, read in NOTE-1208, and their review (LIT-1556). P([Z]) → α^{K+}/∏_{h≥1} K_h! · exp{−αH_N} · ∏_k (N − m_k)!(m_k − 1)!/N! on lof-classes, and the buffet gives the same. It is a statement about the limit: at finite K the expected count of occupied features is below αH_N (THEORY-999), and an ordered truncation of the same limit is a different approximation (THEORY-1041). | Active |
| THEORY-1044 | For the infinite hidden Markov model the beam sampler reaches the posterior in fewer iterations than the single-site Gibbs sampler, and is less sensitive to initialization and hyperpriors, particularly when hidden states persist and emissions are uninformative, at a cost per iteration close to the Gibbs sampler’s | Van Gael, Saatci, Teh and Ghahramani (2008), LIT-1622, read in NOTE-1204. Two synthetic designs (an almost cyclic 4-state HMM, length 800, 20 runs; persistent 4-state HMMs with self-transitions to 0.999, length 4000, 60 starts), a well-log series and a text task. The beam sampler is exact by construction (THEORY-1037); how much faster it mixes is shown only in iterations and by eye. | Proposed |
| THEORY-1045 | On synthetic data from factorial hidden Markov models with three or five hidden chains of two or three states, an unconstrained hidden Markov model with as many states as the chains have joint settings overfits, its test-set excess over the true model rising to 175 bits per observation at five three-state chains against 4.5 for the factorial model trained exactly, while factorial models trained with completely factorized or structured variational E steps are not significantly worse than exact training | Ghahramani and Jordan (1997), LIT-1628, read in NOTE-1203. Four sizes, 15 random parameter sets each, 20 training and 20 test sequences of length 20, four-dimensional, C = 0.0025I, one run per set. In bits per observation over the true model, the K^M-state HMM’s test excess is 2.29, 9.81, 11.57 and 175.35; the exact factorial HMM’s 1.05, 1.26, 2.51 and 4.49; the structured approximation’s 1.04, 0.90, 1.53 and 4.30. It is a result on small synthetic problems the model generated, not on real data or long sequences. | Active |
| THEORY-1046 | In infinite sparse factor analysis, where a binary mask says whether a source is active at a data point and an independent Gaussian value says how strongly, the evidence of that data point for the source being active, with its value integrated out, is σ̂·exp(μ̂²/(2σ̂²)) for the posterior mean μ̂ and standard deviation σ̂ of the value; when the residual has no component along the source’s loading the ratio is σ̂, below one, so the data favour an inactive source over an active one at zero by a factor that the prior on the value sets | Knowles and Ghahramani (2007), LIT-1626, read in NOTE-1209. With y = g x + ε, x ~ N(0, 1), ε ~ N(0, σ_ε² I): ∫ p(y | x) p(x) dx / p(y | x = 0) = σ̂ exp{μ̂²/(2σ̂²)}, σ̂² = σ_ε²/(σ_ε² + g′g), μ̂ = g′ε/(σ_ε² + g′g). It is the Gaussian case only; the Laplacian case is the paper’s (14), checked the same way. It concerns one data point and one source, with the loading known. | Active |
| THEORY-1047 | The curve units of InceptionV1’s mixed3b implement a simple algorithm that can be read off their weights and written down in a few sentences: families of Gabors, lines and early curves, each a set of rotated copies of one unit, tiled along the curve’s tangent, with negative weights against similar shapes of opposing orientation, rotational and scale equivariance reducing the circuit’s more than 50,000 parameters about fifty-fold, so that a network written from this description reimplements them and the description accurately reflects the circuit, as Cammarata, Goh, Carter, Voss, Schubert and Olah claim | Cammarata et al. (2021), LIT-1629, read in NOTE-1207. The article’s account of how curve detectors are built, and its claim that the account is the circuit. The family structure and the echo edit are measured (THEORY-1038); that the description is complete, and that the reimplementation matches the natural units beyond strong cases, is shown by figures only. | Proposed |
| THEORY-1048 v2 | On the Black Queen Hypothesis of Morris, Lenski and Zinser, losing a costly function whose product leaks to neighbours is favoured by ordinary individual selection in large free-living microbial populations, and the loss proceeds until the remaining producers just supply the community, so that most cells come to depend on a rare few with no relatedness, cooperation or collective required | Morris, Lenski & Zinser (2012), LIT-1568, read in NOTE-1212. A loss-of-function mutant invades when its resource saving B = (Q_A − Q_M)/Q_A exceeds its cost C, which falls as other cells’ leaky activity protects it. Because protection falls as producers become rare, the loss is frequency dependent and stops short of community-wide loss. The evidence is Prochlorococcus’s loss of katG and its dependence on a peroxide-removing community. The dependence it produces is one-way, from beneficiaries to helpers, and involves no collective. | Active |
| THEORY-1049 v3 | On McCutcheon and colleagues’ survey, bacterial endosymbionts lose their own cell-envelope and envelope-transport genes together below about 400 kb, and begin to lose translation genes (ribosomal proteins, tRNAs, aminoacyl-tRNA synthetases) below about 200 kb, so that the smallest-genome symbionts cannot be self-sufficient and their membranes, transport and protein synthesis are presumably supplied by the host, as for organelles | McCutcheon, Garber, Spencer & Warren (2024), LIT-1571, read in NOTE-1213. The envelope goes first, near 400 kb, and translation starts to go below about 200 kb, the authors’ “tipping point”. Such symbionts have three-membrane envelopes and among the most biased proteomes in bacteria. They can only work if the host provides what they no longer encode. The host’s role is inferred, not shown: the mechanisms are, in the paper’s word, mysteries. | Active |
| THEORY-1050 v2 | In Athreya, Czuppon and Gokhale’s adaptive-dynamics model of an incipient endosymbiosis, mutual dependence (the product of the partners’ obligacies) evolves ahead of reproductive cohesion (the product of their adhesions) early on, but only under the mapping in which each partner’s free-living growth depends on its own obligacy alone while dissociation depends on both partners’ adhesions; the authors’ own appendix shows the bias vanishing under matched mappings and reversing under the opposite one, and their survey of real symbioses cannot test it | Athreya, Czuppon & Gokhale (2025), LIT-1570, read in NOTE-1211. In the exponential version of the model, all four traits rise monotonically. Each partner becomes more obligate than adhesive, because a gain in adhesion is “damped by the other adhesion” in the dissociation rate. Table S1 shows this is a consequence of that mapping: matched mappings give no bias, and the opposite mapping biases trajectories towards cohesion. The record’s summary of the result, “even when investments are uncorrelated”, is true of the traits’ genetic correlation but not of their functional coupling, which is what decides it. | Active |
| THEORY-1051 v2 | In Athreya, Czuppon and Gokhale’s model of an incipient endosymbiosis, the partner with the larger and faster-growing population evolves faster and becomes fully obligate first, which the authors read as a Red King effect in which the collective’s shared fate aligns interests; with equal within-collective rates for both partners, the other partner’s dependence then stays where it was, rises to full dependence, or falls to none, according to whether partners are born or die inside the collective; and in its simulations dependence rose from zero at the higher collective carrying capacities tried and not at the lowest, under a condition the authors show sufficient and not necessary, so a full transition to a mutually dependent, co-reproducing pair is a parameter-dependent outcome and not the default | Athreya, Czuppon & Gokhale (2025), LIT-1570, read in NOTE-1211. With the symbiont’s population larger and faster, its obligacy reaches 1 first. In the base model the host’s R₀ is then exactly 1, so host obligacy is neutral. With within-collective deaths the host goes fully obligate, and with within-collective births it goes back to independence. Obligacy rose from zero in simulations where the collective’s carrying capacity exceeded about aK_HK_S/d, a condition shown sufficient, not necessary; collective growth rate does not matter. The authors take the model as a null: a transition “is far from an inevitable outcome of the existence of a higher level of selection”. | Active |
| THEORY-1052 | A quasi-static attractor describes an open system only while the drift of that attractor in state space is slow against the system’s slowest relaxation, scaled by the distance to the tipping threshold; rate-induced tipping is the failure of that time-scale separation, and it can occur while the parameter itself moves slowly, if the attractor is sensitive to it, and with no slowing of any mode | Ashwin, Wieczorek, Vitolo and Cox (2012), LIT-1654, read in NOTE-1215. Shown for the linear tipping-radius model, where the sufficient condition for tracking is a rate comparison, and stated for a fast-slow example (“rate dependent tipping occurs when the slow and very slow timescales are no longer separable”). Proposed because for nonlinear systems the paper says “no exact analogy possible” and gives no general condition. It bears on CLAIM-478, whose constraints hold over a window between time scales. | Proposed |
| THEORY-1053 | Under unitary evolution, two states of a quantum system can each leave a record in another system while themselves staying undisturbed only if they are orthogonal or the record does not distinguish them; so the outcomes that can be recorded repeatably form an orthogonal set, a result that uses only unitarity and repeatability and not the Born rule | Zurek (2009), LIT-1640, eq. (5), read in NOTE-1229. From |u⟩|e₀⟩ → |u⟩|e_u⟩ and |v⟩|e₀⟩ → |v⟩|e_v⟩, preservation of the scalar product gives ⟨u|v⟩ = ⟨u|v⟩⟨e_u|e_v⟩, so either the record is no record or ⟨u|v⟩ = 0. Zurek reads this as the origin of the outcome set of the collapse postulate. It does not give single outcomes, probabilities or which orthogonal set is chosen; that is the interaction’s. | Active |
| THEORY-1054 | One arrangement of harmonic particles on a finite graph, with the same wiring, potential and inverse-mass response, gives the discrete wave equation when the integrator stores position and momentum and the discrete heat equation when it stores position alone; both are governed by the symmetrized graph Laplacian, and the coupling data do not decide between them | Spivak (2026), LIT-1649, read in NOTE-1225 from arXiv v2. In the operad ArrSm, harmonic particles wired along a finite directed graph form one closed arrangement with potential Σ(κ_e/2)(q_tgt − q_src)². The phase semantics gives m_v q̈_v = −(L_G q)_v (Proposition 7.4.1) and a symplectic step; the configuration semantics gives m_v(q_v(t+1) − q_v(t)) = −(L_G q(t))_v (Remark 7.4.2). Active: both are short exact computations. It says nothing about time scales, and what differs between the two is a modelling choice, not the coupling. | Active |
| THEORY-1055 | In models of decoherence, the information a small fraction of the environment holds about a system rises steeply to a plateau at the system’s entropy H_S, so many disjoint fragments each carry nearly all of it, and this redundancy is high only for the pointer observable; Zurek identifies it with objective existence, many observers learning the pointer state independently and without disturbing the system, though the paper argues and does not prove that a plateau in mutual information gives each observer the same record | Zurek (2009), LIT-1640, section II and Figs. 2–3, read in NOTE-1229. Redundancy R_δ = 1/f_δ, the number of disjoint fragments each holding (1 − δ)H_S of the information about S, is large for states made by decoherence and absent for random states, and peaks sharply at the pointer observable. Those are model results the review cites. The step from redundancy to objectivity (“Large redundancy implies objectivity”) is an identification. The later caveat, that mutual information alone does not guarantee independently accessible records, is not in the paper. Proposed for that step. | Proposed |
| THEORY-1056 | In angular synchronization with outlier offsets, a polynomial-time spectral relaxation, the top eigenvector of the Hermitian matrix of measured phase offsets, recovers the angles once the share of good offsets exceeds about 1/√n on the complete graph, within a factor √((L − 1)/(2 log₂ L)) of the information bound that limits every algorithm, while exact maximum likelihood is a non-convex search costing O(mLⁿ) exhaustively; in this model the price of recovering the global configuration cheaply instead of optimally is a constant factor in evidence, which vanishes for L ≤ 6 | Singer (2011), LIT-1655, §§2, 4 and 5, read in NOTE-1224 from arXiv v2. The threshold p > 1/√n comes from a cited rank-one deformation theorem adopted to a non-Gaussian mixture and a heuristic comparison with random correlation, confirmed by simulation at n = 100 and 400; the near-optimality ratio compares it with an information bound for a different success criterion. Proposed for both steps. It does not say that recovery is cheap on every graph, under every noise model, or for fine angular resolution. | Proposed |
| THEORY-1057 | Gradient descent with backpropagation, weight decay and Newton’s method are one discrete-time semantics of an operad of potential-carrying lenses, in which the state moves by subtracting the sharpened sum of three pulled-back covectors (from the output, from the input wiring and from the potential); the semantics is an operad functor, so a composite’s update is assembled from its parts’ updates, and backpropagation is that functoriality | Spivak (2026), LIT-1649, read in NOTE-1225 from arXiv v2. Lens internalization (Corollary 3.3.4) and an integrator give operad functors ArrSm → PC (Theorem 4.3.6, Corollary 6.4.1). Under the configuration integrator the state update is q ↦ q − ♯_q(ξ_Q), with ξ_Q the Q*-component of the sum in (58); a parameterized map wired to a loss gives gradient descent (76), a weight-only potential gives weight decay (Proposition 7.2.3), and an inverse-Hessian response gives Newton’s method (67). Active as mathematics. Per datum, deterministic, explicit-Euler; Adam and momentum are conjectures. | Active |
| THEORY-1058 | Given constructor theory’s principles of locality and of classical information, a single further prohibition, that two information observables with mutually disjoint attributes have a union that is not an information observable, is enough for a medium to have information attributes that cannot be distinguished, unclonable and jointly unsharp observables, measurements that are deterministic yet unpredictable, irreducible disturbance by measurement, and locally inaccessible information; quantum information is an instance | Deutsch & Marletto (2015), LIT-1663, §§7–8, read in NOTE-1219. Active as a conditional. The derivations are informal but complete arguments from principles II–IX, and each feature is shown in the paper’s own terms with no probabilities. The principles themselves are conjectures. It does not say that superinformation singles out quantum theory, or that the quantum features are derived from anything not already assumed. | Active |
| THEORY-1059 | The dynamics a coupled cell network admits, restricted to a robustly synchronous pattern, are dynamics admitted by a smaller quotient network whose cells are the synchronized classes, so behaviour of the quotient, including symmetric behaviour the original network has no symmetry to force, appears in the original as synchronous behaviour; the quotient admits more dynamics than restriction produces, and is unique only up to refinement of its arrow types | Stewart, Golubitsky and Pivato (2003), LIT-1674, read in NOTE-1217: the quotient construction (§7), Theorems 8.3, 8.4 and 9.2 with proofs, the counterexample of Remark 7.5 and Example 7.1. Active as mathematics. The quotient describes the dynamics on the invariant subspace exactly, but only a subclass of the quotient’s own admissible dynamics arises that way, and nothing is said about stability transverse to the subspace. | Active |
| THEORY-1060 | Robinson’s claim that sheaves are the canonical data structure for sensor integration rests on an axiomatization, not a theorem: six axioms are posited as what an integrated sensor system must be and a sheaf is defined as whatever satisfies them, the paper calls sheaves one of many co-universal information representations, and its consistency and fusion tools need only a presheaf | Robinson (2017), LIT-1658, read in NOTE-1221 from arXiv v3. A textual finding about the paper, Active as such. The word “canonical” is never defined for sheaves as a sensor model; its technical uses are the standard ones for cohomology. It does not say that sheaves are a poor model, or that no theorem of this kind could be proved. | Active |
| THEORY-1061 | Flack makes downward causation operational as components tuning their behaviour to their own estimates of aggregate variables they collectively compute: weak (apparent) when at least one component tunes to a variable slower than the behaviour producing it, strong (effective) when the variable is predictive, robust, used nearly universally, agreed on and gaining mutual information with the microscopic behaviour; she speaks of a new level only at the strong form, and regeneration of the variable by its use is not among her criteria | Flack (2017), LIT-1630, read in NOTE-1216, §1, §3 and §7. Active as a reading of what the paper proposes, which its text states as lists. It does not say the proposal is right, that it meets any definition of causation (the paper sets that aside), or that the macaque system meets the strong criteria; the evidence for that is in earlier papers not reproduced here. The sharp edge for the record: what reinforces itself in Flack is the convergence of members’ estimates, not the variable’s persistence. | Active |
| THEORY-1062 | On a discourse sheaf, where each agent expresses a private opinion through a linear map into each edge’s space of topics, sheaf-Laplacian opinion diffusion converges to the orthogonal projection of the initial opinions onto the global sections, which are agreement in what each pair expresses and not in what they hold; stable polarized or incomparable private opinions are therefore possible, and when the sheaf has no nonzero global section the only limit is all opinions zero | Hansen and Ghrist (2020; SIAM J. Appl. Math. 2021), LIT-1646, §§2–4, read in NOTE-1222 from the arXiv preprint. Active as mathematics: the convergence is a theorem about a linear heat equation, and the gap between expressed and held opinion is in the definitions and is worked in an example. It does not say that people reach agreement this way, or that an agreement in expression shows anything about what is held. | Active |
| THEORY-1063 | Black-boxing a passive linear circuit, which keeps only the Lagrangian relation its terminals’ potentials and currents can jointly satisfy, is a hypergraph functor from open circuits to Lagrangian relations: the external behaviour of a circuit glued from parts is the relational composite of the parts’ external behaviours, so circuits with the same behaviour are interchangeable in every composite, and the effective relation a composite presents at its boundary is fixed by its parts’ black boxes alone | Baez and Fong (arXiv 2015, TAC 2018), LIT-1644, read in NOTE-1223: Thm 1.1, proved as Thm 7.7, for circuits of passive, linear, two-terminal components over a field with positive elements, inductors and capacitors entering through the Laplace transform with zero initial conditions. The functor is not faithful, which is the point: circuits with one behaviour are identified. It says nothing about nonlinear or active components, and nothing in time-domain terms. | Active |
| THEORY-1064 | In counterexample-guided abstraction refinement, a spurious counterexample locates the distinction its abstraction lacked: walking it forward through the concrete system, the first abstract state where no concrete continuation exists merges the states the trace can reach with the states that have the transition onward, and splitting them removes the counterexample; for finite-state programs and ACTL* properties whose counterexamples are paths or loops, repeating check and split ends in a real counterexample or a proof | Clarke, Grumberg, Jha, Lu and Veith (2000), LIT-1652, read in NOTE-1231 from the authors’ manuscript of the CAV paper. Active: the test for spuriousness (Lemma 1), the three-way cut at the failing state and the termination argument are given in full. The NP-hardness of the coarsest split is stated with its proof omitted, and the loop case rests on a theorem proved elsewhere. It does not say that the split found is the smallest, or how many rounds are needed. | Active |
| THEORY-1065 | In a coupled cell network, a pattern of synchrony is invariant under every dynamics the network’s architecture admits if and only if its partition of the cells is balanced, each cell of a class receiving, through each kind of arrow, the same number of inputs from each class; symmetry is one way to get balance and not the only one, so robust synchrony occurs in networks with no symmetry and among cells with no coupling between them, and the invariance says nothing about whether the pattern attracts | Stewart, Golubitsky and Pivato (2003), LIT-1674, read in NOTE-1217 from the accepted version: Theorem 6.5 with proof, Lemma 6.3, worked examples without symmetry (Figures 3, 9, 15, 19). Active as mathematics. It generalizes THEORY-276’s orbit clusters. “Robust” means invariant for the whole admissible class, not stable, and not invariant for one model family; the paper studies “existence, not stability”. | Active |
| THEORY-1066 | In constructor theory, a set of attributes is an information variable when every permutation of it and its cloning are possible tasks, and distinguishability is defined afterwards, as the possibility of mapping a variable onto an information variable; so information is fixed by counterfactual properties of a substrate without presupposing distinguishability, and instantiating it is stated as an intrinsic property of the substrate in the sense of referring to no other specific substrate | Deutsch & Marletto (2015), LIT-1663, §§3–5, read in NOTE-1219. Active as a fact about the construction: the definitions are given in that order, and the base they give the recursion of (1.1) is checkable on the page. It does not say that these notions are the intuitive ones, which the authors disclaim, nor that the principles built on them hold. Its “intrinsic” excludes reference to a specific other substrate, not to generic ones, which the cloning task and (5.1) both use. | Active |
| THEORY-1067 | In angular synchronization from m pairwise offsets, each exact with probability p and otherwise uniform over L values, no estimator of any computational cost can recover all n angles with small error when p is below about √((n/m)·2 log₂ L/(L − 1)), nor an angle of average degree below about √((n/m)·log₂ L/(L − 1)), because each offset carries at most I(L, p) ≈ ½(L − 1)p² bits; below these thresholds a global configuration that exists is not determined by the pairwise evidence, whatever the resources spent on finding it | Singer (2011), LIT-1655, §5, read in NOTE-1224 from arXiv v2. Active as mathematics: Fano’s inequality applied to an explicit entropy count, asymptotic in m, n → ∞, p → 0 with L fixed. The bound is loose (it ignores the dependencies among offsets) and covers exact recovery and per-angle recovery, not partial correlation, which the eigenvector method achieves below it. It says nothing of what a bounded algorithm can do above it. | Active |
| THEORY-1068 | In the founding statement of relational quantum mechanics the states and values of systems are relative to other systems, but the systems are not: the world is assumed decomposed, possibly in several ways, into systems each characterized by the questions that can be asked of it and a finite information capacity, so the relata precede the relations, as an assumption and without an ontology of events | Rovelli (1996), LIT-1635, read in arXiv v2 in NOTE-1227, §§II.C, III.A–B, III.D and IV.A. Active as a textual fact about the paper. It bears out, for 1996, what THEORY-1071 takes from Faye and Jaksland, who quote later texts for it. It does not say that RQM must keep systems prior, nor that the systems are uniquely given: the decomposition is assumed, not argued, and allowed to vary. | Active |
| THEORY-1069 | In a von Neumann measurement the measuring variable’s information about the measured variable grows continuously under the unitary coupling, in Di Biagio and Rovelli’s model as I_{A:B}(t) = sin²(ωt)H_A, so the discontinuity of a quantum measurement lies only in a threshold on when information counts as a fact; with an idealized pure ready state a fact conditional on a pointer value appears at once, which they attribute to the idealization | Di Biagio and Rovelli (2025), LIT-1676, read from arXiv v2 in NOTE-1214, §VII and App. B. Active as mathematics: (B7) follows from (B6), which I rederived; (B8) as printed has a sign error, and the correct form is I_A^max − cos²(ωt)H_A. The continuity is of the expected quantities. A conditional relative fact appears at once in the ideal model, and the full-rank case that would remove that is described, not computed. The authors say the point is not specifically quantum. | Active |
| THEORY-1070 | For a weighted cellular sheaf of finite-dimensional vector spaces on a finite cell complex, the kernel of the degree-k Hodge Laplacian is the k-th sheaf cohomology, in degree 0 the space of global sections, and the linear flow ẋ = −Δ^k x converges exponentially to the orthogonal projection of its initial state onto that kernel, each eigencomponent decaying at its own eigenvalue; the inner products on the stalks are part of the data, so the same sections can come with different rates, and the Laplacian does not determine the sheaf | Hansen and Ghrist (2019), LIT-1659, read in NOTE-1233 from arXiv v2: Theorem 3.1 (discrete Hodge theory), H^0 ≅ Γ (p. 7) and Proposition 8.1 (the flow), each with a proof; Fig. 3.1 for the Laplacian not determining the sheaf. Active as mathematics. The paper does not speak of relaxation rates or time-scale separation, does not say what produces the restriction maps, and treats only linear flows of a fixed Laplacian. | Active |
| THEORY-1071 | Quantum mechanics does not entail agential realism: Bohmian mechanics reproduces its predictions with an ontology of individual particles on determinate trajectories, and relational quantum mechanics, the interpretation Barad names as closest, makes values relational while keeping the systems prior to their interactions | Faye & Jaksland (2021), LIT-1672, read in NOTE-1220, §5. Active: the non-entailment follows from the existence of an empirically equivalent interpretation with a different metaphysics, and the authors do not promote that interpretation. It does not say agential realism is inconsistent with quantum mechanics; that is THEORY-1091, a separate and weaker argument. | Active |
| THEORY-1072 | In Simon’s analysis, whether a problem is well structured is a relation between the problem and a bounded solver, judged by practicable rather than in-principle computability, so it comes in degrees and has no sharp boundary; on that standard even theorem proving and chess fail some of the conditions, chess is well structured in the small and ill structured in the large, and problems presented by the world become well structured only in being prepared for a solver | Simon (1973), LIT-1634, read in NOTE-1232 from a scan of the published article. Active as a conceptual argument the paper makes in full: six conditions for a well structured problem, read with condition 6 as practicable computation, worked through for theorem proving and chess. It does not say that structuring is the whole of problem solving, which Simon rejects, or that any problem is ill structured for every solver. | Active |
| THEORY-1073 | An aggregate variable much slower than the behaviour producing it becomes an environment the components tune to whether or not it summarizes the underlying regularities well, which helps coordination; if it summarizes them poorly the system likely fails in the end, later the larger the separation | Flack (2017), LIT-1630, read in NOTE-1216, §6. Argued informally, with social institutions and the macaque power distribution as illustrations, and no model or data. Proposed. It does not say slowness makes an aggregate accurate, or that separation alone makes the components use it: in Flack the aggregate constrains only through the components’ tuning to it. | Proposed |
| THEORY-1074 v2 | In Di Biagio and Rovelli’s relational account two classical subsystems’ perspectives merge, agreeing on a variable’s value and on each other’s, when they couple to that variable or to each other, and a coupling to a complementary variable can remove a relative fact from a perspective that did not interact; that this answers the combination problem and keeps perspectives consistent is shown only in worked examples computed relative to a single outside system | Di Biagio and Rovelli (2025), LIT-1676, read from arXiv v2 in NOTE-1214, §VI and Apps. D–E. The merge, and the disturbance of a third party’s relative fact, are computed in a three-system example and in Wigner’s friend. The general claims, a solution to RQM’s combination problem and consistency of perspectives, are asserted, not shown; whether they hold is THEORY-1213, Proposed. Every computation is relative to one outside system, where agreement is automatic. This is the same gap THEORY-621 and THEORY-1080 name. | Active |
| THEORY-1075 | In relational quantum mechanics as Di Biagio and Rovelli define it, a fact relative to one system is stable for another, so that the other may sum over it classically, only approximately and only relative to that other system: decoherence of the first system by an environment the second cannot reach gives the classical rule to order of the environment states’ overlap, a differently coupled system may still see interference, and a fact can be stable for a system for which it is not yet a fact | Di Biagio and Rovelli (2021), LIT-1666, read in NOTE-1226, §1 (pp. 2–6). Active: the definitions are the paper’s, and the result follows in a few lines from a partial trace (eqs. 5–8) under two stated conditions, ε small and the third system not interacting with the environment. It does not say that stable facts are absolute, that decoherence settles which outcome occurred, or what fixes the division into systems. | Active |
| THEORY-1076 | For Bohr a phenomenon is the observation obtained under a specified experimental arrangement, epistemic and derivative, with atomic object and instrument presupposed real; his relational holism is epistemic, and the subject–object, knower–known and word–world dualisms are presupposed by his account, so Bohr’s authority does not support agential realism | Faye & Jaksland (2021), LIT-1672, read in NOTE-1220, from Bohr’s writings and the secondary literature. Active as exegesis: Bohr’s own definitions of “phenomenon” (1938, 1949) and the convergence of realist and antirealist readings that Bohr never denied atomic objects. The dualisms half is interpretive and weaker. It does not say that Barad’s view is false, only that it is not Bohr’s. | Active |
| THEORY-1077 | On a presheaf of pseudometric spaces, the consistency radius of an assignment, the largest distance between an observation and the restriction of another, is zero exactly for assignments induced by global sections (in metric spaces) and, when the restrictions are K-Lipschitz, bounds the assignment’s sup-distance from every global section below by ε/(1 + K); so fusing data into a consistent state must move it at least that far, and the bound needs no sheaf condition | Robinson (2017), LIT-1658, Definition 20 and Propositions 21 and 23, read in NOTE-1221 from arXiv v3; both proofs checked. Active as mathematics. It does not say that the nearest global section is unique (the paper’s Proposition 25 claims so for Banach sheaves and the proof does not reach it), that the radius locates a fault, or that a small radius means the data are right. | Active |
| THEORY-1078 | Constructor theory puts constraint in two places: a principle is a law that constrains other laws and is tested through its rivals, and a constructor is a physical thing that keeps its ability to cause a transformation; a task is possible when the laws set no limit, short of perfection, on how well it could be performed and that ability retained, so possibility needs no actual constructor, and constructor-theoretic statements mention none | Deutsch & Marletto (2015), LIT-1663, §§1–2 and footnote 1, read in NOTE-1219. Active as a reading of the paper’s definitions, which are explicit. It bears on A11’s remark that constructor theory “could sharpen” what the record means by “a constraint being real”, and it splits that notion. A possibility is a fact about the laws, which no particular thing realizes; a constructor is realized, approximate and deteriorating. It does not say that the framework’s basic principle I is true, nor that a law of possibility is, or is not, a constraint realized by something (CLAIM-477). | Active |
| THEORY-1079 | An open system can tip away from an attractor that exists, keeps its stability and keeps its basin at every frozen value of its parameter, when the attractor moves faster than the system can track it; with steady drift what bifurcates is the ability to track, in a co-moving frame, not the attractor, and the critical rate depends on the relaxation rate, the distance to the tipping threshold and the starting state | Ashwin, Wieczorek, Vitolo and Cox (2012), LIT-1654, read in NOTE-1215 from the corrected arXiv v5. Active as mathematics: shown in a linear model with a fixed stable matrix (so no bifurcation and no noise), in normal-form examples worked exactly, and in a fast-slow system whose equilibrium is unique and globally stable. It does not say that a system that tips is lost for good, that the threshold is a basin boundary, or that any real system has tipped this way. | Active |
| THEORY-1080 v2 | In relational quantum mechanics as Rovelli first stated it, the relation between two observers’ descriptions is itself a quantum fact relative to a third system, so no observer’s view can be deduced from another’s and there is no description in toto, only a net of partial descriptions; the views are held consistent only in that the third system predicts correlated outcomes, which is shown for a single measurement and asserted in general | Rovelli (1996), LIT-1635, read in arXiv v2 in NOTE-1227, §§II.D, III.D, IV.A–B. The first half (no deducible relation between views, no in-toto description) is Rovelli’s stated position, well supported by his text. The second half reports that consistency is shown for one case (von Neumann’s correlation, p. 9) and left to the reader in general (p. 15); whether it holds in general is THEORY-1222, Proposed. Rovelli’s own relativity analogy breaks where relativity supplies an invariant, which bears on QUESTION-021 by analogy only. | Active |
| THEORY-1081 v2 | Di Biagio and Rovelli locate the Frauchiger–Renner contradiction and the violation of the Local Friendliness inequalities in one step, a superobserver using facts relative to a friend he holds in full quantum control as if they were his own, which is the classical sum rule applied where those facts are not stable for him; they base quantum ontology on facts relative to systems rather than on stable facts, arguing that stability is itself relational and only approximate and counting the Local Friendliness violation as evidence, with an absolute macroreality emerging only approximately and only relative to systems for which decoherence is strong | Di Biagio and Rovelli (2021), LIT-1666, read in NOTE-1226, §2 (pp. 7–11). The translation of Frauchiger and Renner’s assumption (C) and of Bong et al.’s absoluteness of observed events into the use of eq. (3) across contexts is the paper’s and is clear. That nothing else goes wrong is cited to others, inter-observer agreement is one sentence, and an agent reasoning about himself is left undone. What the paper argues is held; whether relative facts cohere in general is THEORY-1230’s question. | Active |
| THEORY-1082 | On a connected graph whose edges carry phase shifts αᵢⱼ = −αⱼᵢ, the edge relations zⱼ = e^{iαᵢⱼ}zᵢ have a common nonzero solution, equivalently the twisted Laplacian Lα = δα*δα has a zero mode, exactly when the phase accumulated around every cycle is 0 mod 2π; otherwise each relation can be met alone but not all together, and the smallest eigenvalue of Lα, positive, measures the residual incompatibility, which on an isolated ℓ-cycle is largest at holonomy π | Torres-Hugas, Duch, Gómez and Arenas (2026), LIT-1668, read in NOTE-1218 from the arXiv preprint v2. The criterion is stated in the paper with an energy argument (pp. 2–3) and is the standard one for discrete magnetic and connection Laplacians, which it cites; the spanning-tree step the paper omits is written out below. The isolated-cycle spectrum is in closed form (eqs. 29–32). Both were checked numerically. Active: a theorem, with the qualification that it concerns the relaxed linear problem, not the phase dynamics. | Active |
| THEORY-1083 | Barad holds agential realism to be naturalized metaphysics justified by quantum mechanics and applied once, to the one reality, with its scope extended to the lifeworld; she rejects both reading it as an analogy and reading it as a template that quantum mechanics and other domains each instantiate | Jaksland (2024), LIT-1673, read in NOTE-1230, from Barad’s own statements (2007, 24 and 85, with her dismissals of analogy at 2007, 6, 7, 18, 24, 70 and 88). Active as a reading of what Barad holds, which is well supported by her text as quoted. It does not say that the conception she holds is sound: that rests on agential realism being correct as quantum mechanics, which Faye and Jaksland dispute (THEORY-1071). It does say that a use of her concepts outside physics by structural comparison is a use she disowns. | Active |
| THEORY-1084 v2 | Simon proposes that ill structured problems can be handled by an alternation between a solver working on a problem that is well structured at each moment and a recognition and retrieval system that keeps modifying the problem space from memory or the environment, that a serial solver gains nothing by assembling the problem space at the outset, and that nothing but the size of the knowledge base may separate ill from well structured problems, so that no qualitatively new mechanisms are needed | Simon (1973), LIT-1634, read in NOTE-1232. The alternation is described for an architect, matched to a 1923 account of battleship design by an organization and to the NSS chess program, and argued from the seriality of the solver; nothing is implemented or tested, and Simon states the last part as what his analysis “suggests” and as “reason to be optimistic”. Active as a report of the proposal; whether it is right, which wants a test, is THEORY-1216, Proposed. | Active |
| THEORY-1085 | In Toner and Tu’s hydrodynamic theory, a flock’s ordered state is a broken continuous symmetry of a coarse-grained velocity field: speed fluctuations relax in a finite time of order 1/α and are dropped, leaving as slow degrees of freedom the transverse velocity and the conserved density, which propagate as sound at ω = ±cq⊥; no individual member appears in the description, which is offered for a universality class of microscopic rules | Toner and Tu (1995), LIT-1670, read in NOTE-1228 from the arXiv preprint. Active as a statement of what the theory is: its variables, the degree of freedom it eliminates and why, and the modes that remain, all in the text (pp. 3–8). It does not say that the theory’s exponents are right (THEORY-1095), that the universality claim holds, or that the order so described is an agent or an individual. | Active |
| THEORY-1086 | A fundamental metaphysics bears on the metaphysics of the lifeworld only through features that admit no approximation; without any, a relational world can approximate one of separable individuals, and the independence of social theorizing from fundamental metaphysics is then real but contingent, on the size of Planck’s constant, not principled | Jaksland (2024), LIT-1673, read in NOTE-1230, reconstructing an argument Barad “only ever alludes to”. It is a conditional and the author leaves its antecedent open: whether any ontological feature is all-or-nothing is “an open question”. He finds individualism “immediately more agreeable” as approximable, and the dualisms the harder case. The contingency half is argued (a counterfactual on Planck’s constant); the no-approximation half is a candidate list, not a demonstration. | Proposed |
| THEORY-1087 | In the symmetric Sakaguchi–Kuramoto model on a triangle and a pentagon sharing one vertex, the lag α gives each ℓ-cycle a phase-independent path mismatch (ℓ − 2)α, and the remote-synchronized locked branch passes through an exact two-group state at α = π/3, where the pentagon’s mismatch reaches π; but that branch has already lost transverse stability, in the pentagonal symmetry sector, at αc ≃ 1.0164, so the point of maximal cycle frustration marks the geometry of the phase relations, not the end of the synchronized pattern | Torres-Hugas, Duch, Gómez and Arenas (2026), LIT-1668, read in NOTE-1218 from the arXiv preprint v2. The mismatch (ℓ − 2)α is a three-line derivation (eqs. 15–18); the two-group state at π/3 is exact algebra (eqs. 38–40); the threshold αc is a numerical continuation with det M⊥ = 0 (Supplementary Material). All three were reproduced. Active for this motif and branch; the paper’s wider reading, that remote synchronization is a manifestation of cycle-level constraints, is not what this says. | Active |
| THEORY-1088 | When the expression maps of a discourse sheaf diffuse to reduce disagreement, with opinions held fixed they converge to the nearest sheaf, in Frobenius distance, of which the opinions are a global section, so apparent consensus is reached by changing what is said (“learning to lie”); with opinions diffusing too the joint flow is gradient descent on ½‖δx‖², and conserved diagonal blocks of αδᵀδ − βxxᵀ keep the opinions from collapsing to zero; nothing in either flow checks an expression against the opinion it expresses | Hansen and Ghrist (2020; SIAM J. Appl. Math. 2021), LIT-1646, §§8–9, read in NOTE-1222 from the arXiv preprint. Active as mathematics: Theorems 8.1, 9.3 and 9.4 and Lemma 9.1. Theorem 9.3’s proof is right only for α = β as printed; with the α, β weights it holds generally, which was checked numerically in the reading. The degeneracy guards are internal to the loop: minimal change and a conserved quantity, not evidence from outside it. | Active |
| THEORY-1089 | In a passive linear network, eliminating interior nodes by the principle of minimum power, which over a general field with positive elements is stationarity, takes a Dirichlet form to a Dirichlet form on the remaining nodes, linearly in their values; eliminating one node s adds c_is·c_js/Σ_k c_ks to each coupling c_ij, so two resistors in series act at their ends as one of resistance r_AB + r_BC; composing Dirichlet forms by this elimination is associative but lacks identities, because an ideal wire of zero impedance has no power functional | Baez and Fong (arXiv 2015, TAC 2018), LIT-1644, read in NOTE-1223: Thm 3.3, Lemma 3.4, Example 2.9 and Sec. 3.3. The elimination is what is usually called Kron reduction, a name the paper does not use. Over ℝ(s), with inductors and capacitors, the “minimum” is a formal stationarity condition, Kirchhoff’s current law at interior nodes. The absence of identities is computed for a one-element set and asserted as typical otherwise. | Active |
| THEORY-1090 | Eliminating an interior vertex of a cellular sheaf on a graph can leave its boundary a space of consistent assignments that no sheaf on the boundary vertices has: the interior can impose a constraint among boundary vertices that no set of pairwise compatibility conditions expresses, so Kron reduction, which turns the Laplacian of a connected graph into a graph Laplacian on any set of boundary vertices, fails for sheaves in general and holds when every vertex stalk has dimension at most one | Hansen and Ghrist (2019), LIT-1659, §4.2 (pp. 18–21), read in NOTE-1233: a worked three-leaf star with a two-dimensional centre, and a closure theorem for the scalar-stalk case. Active as mathematics; the argument was checked. It is about the space of sections, a static fact; it does not say how often the obstruction arises, what structure would express the reduced constraint, or anything about dynamics. | Active |
| THEORY-1091 | Agential realism has no answer to the measurement problem as it stands: holding that measurement never disentangles apparatus and object, it cannot borrow relational quantum mechanics’ treatment of the wave function as bookkeeping without giving up the ontological holism, and its appeal to an improper mixture does not explain why one value is found | Faye & Jaksland (2021), LIT-1672, read in NOTE-1220, §5. Proposed: the authors present it as a challenge (“There might be other more subtle ways”), and conclude only that consistency with quantum mechanics is unshown (“a leap of faith”), not that agential realism is incoherent. The exchange of 2026-10-27 reported it as “an unresolved measurement problem”, which is the strength the text supports. | Proposed |
| THEORY-1092 | Read over the sensor domains, the discrepancies between each observation and the restrictions of others can single out a faulty sensor where the consistency radius alone does not: in Robinson’s simulated search, a 2° bearing bias was attributed to the right sensor, without prior knowledge of it, because every large discrepancy involved that sensor’s domains, while the radius was lower than in the unbiased case | Robinson (2017), LIT-1658, Example 24, Case 2 (pp. 26–28 of arXiv v3), read in NOTE-1221. One simulated case, one noise realization, read from a figure. Proposed until a stated procedure is tested over trials, including faults in the restriction maps, which enter the discrepancies in the same way as faults in the data. | Proposed |
| THEORY-1093 | In Di Biagio and Rovelli’s reformulation of relational quantum mechanics a relative fact is a conditional probability concentrated on one value: A is a fact relative to B when the relative information I_{A|B} = I_A + I_{A:B} is maximal; since only commuting variables have a joint distribution, perspectives belong to commutative subalgebras of observables, not to quantum systems, so a qubit has none, and the joint distribution is itself relative to a further system, so the relativity iterates | Di Biagio and Rovelli (2025), LIT-1676, read from arXiv v2 in NOTE-1214, §§II–V and IX. Active as a statement of the paper’s definitions and of what follows from them: eq. (7) is an identity, and the restriction to commuting variables follows from the existence of joint distributions. It does not say that this resolves the problems the authors list, that observers play no role in fixing what counts as a fact, or that the choice of subalgebra is given by the physics. | Active |
| THEORY-1094 | In counterexample-guided abstraction refinement the property and the concrete system are fixed inputs: the property’s atomic formulas help build the first abstraction and no abstraction may merge states that disagree on them, every refinement only splits classes toward the concrete state space, and a real counterexample ends the procedure; so the loop revises which of the concrete system’s distinctions the model draws, never the property or the space of possible answers | Clarke, Grumberg, Jha, Lu and Veith (2000), LIT-1652, read in NOTE-1231. A textual fact about the algorithm as specified in §§3–4, and the exact form of the limit the exchange of 2026-10-27 (A16 §6) gave for CEGAR as the formal neighbour of inquiry as specification (CLAIM-470). It does not say that a property cannot be revised by anyone, only that no step of this procedure does it. | Active |
| THEORY-1095 | In Toner and Tu’s hydrodynamic model of a flock, true long-range orientational order survives in two dimensions, where the Mermin–Wagner theorem forbids it at equilibrium and the model’s own linearized theory loses it, because the convective coupling of the velocity field to its own transport, relevant below four dimensions, keeps the transverse velocity fluctuations bounded; the authors’ heuristic is that motion keeps changing each member’s neighbours, so originally distant members come to interact | Toner and Tu (1995), LIT-1670, read in NOTE-1228 from the arXiv preprint. The linear theory’s loss of order in d ≤ 2 and the relevance of the convective nonlinearity below d = 4 are calculations. The survival of order in d = 2 follows from χ = −1/5 < 0, which is exact only if a cubic vertex stays irrelevant (“we strongly suspect”), or from χ = (z − d)/3 with z < 2, which is expected “on physical grounds”. The change-of- neighbours mechanism is a heuristic. Proposed for those two steps. | Proposed |
| THEORY-1096 | Blackwell’s comparison of experiments, its easy direction: an experiment is a family of distributions indexed by a common parameter, and if one experiment is a garbling of another by a Markov kernel, every risk attainable with the garbling in any decision problem with bounded losses is attainable with the original, on any outcome spaces | Split from THEORY-156 by the status review of 2026-10-27 (ADR-057). THEORY-156’s equivalence needs a second proof of the general converse and stays Proposed. Ten of its twelve dependents used only its definitions (an experiment, a garbling, the informativeness order), or only the easy direction, that a garbling never helps a decision-maker free to choose any rule. The easy direction holds on any outcome spaces, and its proof is two lines, re-derived below under ADR-047 v2’s ruling, which ADR-057 keeps. It is Theorem 3 of Blackwell (1953), LIT-781, read in NOTE-595, and Blackwell’s 1951 result. The finite converse is THEORY-717, Active. | Active |
| THEORY-1097 | A Markov blanket, in any formulation including sparse coupling at nonequilibrium steady state and time-varying blanket states, does not individuate a system: where it falls is fixed by modelling choices made before it is found, so it presupposes the boundary it is used to find, and it cannot represent a boundary the system produces | The wider claim dropped when THEORY-073 was narrowed to Friston’s 2013 formulation and promoted on 2026-10-27 (ADR-047 v4: a narrowing’s dropped claims go to Proposed entries). Both critiques argue the general form, and the record holds neither of the later formulations it would have to reach. Its promote_when is THEORY-073’s own, moved here unchanged. | Proposed |
| THEORY-1098 v2 | On Karnkowska and colleagues’ genome analysis, the oxymonad Monocercomonoides exilis lost its mitochondrion only after the organelle’s essential functions had been removed one by one, Fe–S cluster assembly to a bacterial-type SUF system shared with mitochondriate relatives and then the glycine cleavage system by loss, and the loss left the rest of the cell canonical, with no compensating changes found | Karnkowska et al. (2019), LIT-1574, read in NOTE-1243. The SUF replacement of the mitochondrial Fe–S pathway is shared by all examined Preaxostyla, including relatives that keep a mitochondrion-related organelle, and those relatives’ organelle still houses the glycine cleavage system that M. exilis lacks. So the organelle lost its jobs in at least two steps before it was lost. Apart from the mitochondrion, peroxisomes and mitophagy, the cell’s systems are those of an ordinary eukaryote. The order is inferred, not dated, and absence is limited by annotation. | Active |
| THEORY-1099 v2 | On Kay and colleagues’ relaxed-clock dating of pre-LECA gene duplications, most duplications in eukaryotic gene families of archaeal origin, including actin, tubulin, vesicle-trafficking and nuclear-targeted families, predate the onset of duplications in genes of alphaproteobacterial origin at about 2.2 billion years ago, which the authors take as the start of mitochondrial endosymbiosis, so the host was elaborating its cytoskeleton, endomembranes and nuclear machinery before the mitochondrion; each date is a maximum age for its paralogues’ functions, many intervals reach below 2.2 billion years, and the order of phagocytosis and the mitochondrion is left open | Kay et al. (2026), LIT-1566, read in NOTE-1234. A dated species tree places nFECA at 3.05–2.79 Ga, mFECA at 2.37–2.13 Ga and LECA at 1.80–1.67 Ga. Against an endosymbiosis marker at about 2.2 Ga, 85% of archaeal-origin duplications are older, and most non-alphaproteobacterial bacterial duplications are younger. The authors reject mitochondria-early scenarios and argue against serial endosymbiosis. The sharp edges are that duplication dates bound functions from above, that the priors shape which family can be older, and that the authors themselves cannot order phagocytosis and the mitochondrion. | Active |
| THEORY-1100 v2 | On Sørensen and colleagues’ review, a bacterial endosymbiont becomes genetically integrated, the authors’ mark of an organelle, when nuclear genes whose products are imported into it functionally replace essential genes it has lost, and this does not require gene transfer from the endosymbiont: in the Paulinella chromatophore and the nitroplast, the two systems with hundreds of imported proteins, many of which fill gaps left by lost genes, the imported proteins come mostly from the host’s own genes or from other bacteria, and in the nitroplast no gene transfer from the endosymbiont has been found | Sørensen, Stiller, Kröninger & Nowack (2025), LIT-1560, read in NOTE-1241. Protein mass spectrometry of isolated endosymbionts found hundreds of host proteins imported into Paulinella’s chromatophore and more than 350 into the nitroplast, where they fill gaps left by lost genes. In Paulinella the imported proteins come mostly from the host’s own genes, with some from gene transfer from the chromatophore and from other bacteria. In the nitroplast no gene transfer from the symbiont has been found at all. So the route to an organelle is import, and the endosymbiont’s genes need not move. The origins are stated in summary, not counted, and the import mechanisms are unknown. | Active |
| THEORY-1101 v3 | Tobiasson, Luo, Wolf and Koonin find, on 5,850 eukaryotic gene stems, that normalized stem length does not behave as a clock of acquisition time: alphaproteobacterial stems are longer than Asgard ones for the 70% of stems below 0.3 and shorter only above 0.35, oxidative-phosphorylation genes presumed acquired together vary by more than two orders of magnitude, and information-processing genes have short stems; they conclude that even normalized stem lengths are set primarily by factors other than acquisition time, at least over the long timescales analysed, and suggest that adaptation after acquisition lengthens stems | Tobiasson, Luo, Wolf & Koonin (2026), LIT-1558, read in NOTE-1242. They test the stem-length method of Pittis and Gabaldón on their own trees and reproduce its mitochondrion-late signal only for long stems. Below 0.3, where 70% of stems lie, the order reverses, and genes presumably acquired together scatter widely. They conclude that “even normalized stem lengths are determined primarily by factors other than the gene acquisition time”. The paper still favours a late mitochondrion, on other grounds. | Active |
| THEORY-1102 v2 | On Pittis and Gabaldón’s stem-length analysis of the LECA proteome, families of alphaproteobacterial origin and mitochondrial location sit closer to their prokaryotic relatives, after correction for each family’s rate, than families of other bacterial origin (P = 0.044), which sit closer than archaeal families, and the authors read this as late acquisition of the mitochondrion by a host whose proteome was already chimaeric, under their stated assumption that rates before and after LECA are correlated | Pittis & Gabaldón (2016), LIT-1595, read in NOTE-1240. Of 1,078 LECA families, bacterial ones have shorter normalized stems than archaeal ones (P = 1.38e-25), and alphaproteobacterial ones shorter than other bacterial ones (P = 0.044). Origin tracks location: alphaproteobacterial with the mitochondrion, other bacterial with endomembranes, archaeal with the nucleus. A plastid control runs the right way. The sharp edges are that stem length measures distance to the closest sampled relative, so sampling can move it, and that the chimaeric host could have come from partners or from transfer, which the paper cannot tell apart. | Active |
| THEORY-1103 v2 | On Shigenobu and colleagues’ genome of Buchnera sp. APS, the aphid symbiont keeps the genes for the amino acids its host cannot make and has lost almost all of those its host can, uses host-made glutamate and aspartate as precursors, and lacks phospholipid synthesis and nearly all its own transcriptional regulators, so that its metabolism interlocks with the host’s and it presumably lives only inside the bacteriocyte, a state reached by gene loss from an E. coli-like ancestor | Shigenobu et al. (2000), LIT-1596, read in NOTE-1236. The first complete genome of an obligate insect endosymbiont: 640,681 bp, a subset of E. coli’s. What is shown is gene content. The interlocking of host and symbiont metabolism is inferred from it and from earlier physiology. That Buchnera cannot live outside the bacteriocyte, and that the host supplies its membrane lipids, are the authors’ inferences. The paper names no mechanism of loss beyond a homeostatic niche: it says nothing of drift. | Active |
| THEORY-1104 v3 | In Tobiasson, Luo, Wolf and Koonin’s constrained-tree survey of widespread eukaryotic protein families, Asgard archaea are the largest single prokaryotic source, with about half the likelihood weight in the best-resolved families and the lead in nearly every functional system, while Alphaproteobacteria contribute a small, coherent set centred on the mitochondrion and other bacteria about a third of families, scattered across functions with no pathway led by one donor except a narrow Myxococcota signal in nucleotide-sugar and nicotinate metabolism; the authors read this as one Asgard host lineage, one endosymbiont and piecemeal gene transfer rather than further symbioses | Tobiasson, Luo, Wolf & Koonin (2026), LIT-1558, read in NOTE-1242. In 4,290 well-resolved eukaryotic–prokaryotic clusters, Asgard takes 50% of likelihood weight and leads in almost every functional class. Alphaproteobacteria account for mitochondrial translation, oxidative phosphorylation and 4Fe-4S assembly. About a third of clusters point elsewhere, with no functional pattern except a narrow Myxococcota signal. The authors infer a complex Asgard ancestor, a late mitochondrion and “no indication of another symbiotic event”. The composition is shown; the scenario is read off it. | Active |
| THEORY-1105 v3 | In Bernabeu, Manzano-Morales, Marcet-Houben and Gabaldón’s reconstruction of the last eukaryotic common ancestor’s proteome, two bacterial phyla besides the mitochondrial ancestor, Myxococcota and Planctomycetota, each account for a share of the proteome comparable to that of Alphaproteobacteria and Asgard archaea under thresholds calibrated on those accepted partners, and stem-length distributions order the acquisitions as waves, Asgard first, then Planctomycetota, then the mitochondrial ancestor and Myxococcota together; the authors read this as serial associations with several partners, while conceding that their data cannot say whether any donor was a symbiont | Bernabeu, Manzano-Morales, Marcet-Houben & Gabaldón (2026), LIT-1561, read in NOTE-1237. Under thresholds chosen to maximize assignments to Alphaproteobacteria and Asgard, Myxococcota (3.92% of the proteome) and Planctomycetota (2.24%) pass in every dataset, beside Alphaproteobacteria (3.99%) and Asgard (3.28%). A control removing Alphaproteobacteria from the database does not reproduce their pattern. Stem lengths put Planctomycetota before the mitochondrion. The authors “challenge models depicting eukaryogenesis as a one-off event resulting from a binary symbiotic interaction”, and also say their data “do not provide information on the host or endosymbiotic nature of any partner”. | Active |
| THEORY-1106 v2 | Campbell and colleagues report, from four cicada species with five or six eggs each, that Hodgkinia cells per egg range from about 4,900 in a species with one Hodgkinia lineage to about 30,000, some six times as many, in Magicicada septendecim, whose Hodgkinia has split into many interdependent lineages and the only species that differs significantly, while Sulcia numbers are not raised, the transmission route is the same, and every egg sampled carries every lineage tracked by marker genes; the authors take the raised titre as a host adaptation that compensates for the symbiont’s fragmentation, and a cost of it | Campbell, Łukasik, Meyer, Buckner, Simon, Veloso, Michalik & McCutcheon (2018), LIT-1590, read in NOTE-1235. Measured: Hodgkinia cells per egg from 4,889 in a single-lineage cicada to 30,154 in M. septendecim, with Sulcia at 2,572 to 5,643; marker genotypes present in every egg sampled; the same route under the light microscope. Not shown: a trend across complexity beyond M. septendecim, or that splitting came first. The authors also speculate that a larger transmitted population weakens bottlenecks and could feed further splitting. | Active |
| THEORY-1107 v2 | On Sørensen and colleagues’ scenario, an endosymbiont becomes an organelle in steps: the host first targets effector proteins into it; an imported host protein redundant with one of its functions then lets the endosymbiont’s own gene decay, making it dependent; and a general import pathway, once evolved, brings in hundreds of proteins; this genetic integration arises only in permanent, vertically transmitted associations, and host effector control without vertical transmission, as in rhizobia, does not lead to it | Sørensen, Stiller, Kröninger & Nowack (2025), LIT-1560, read in NOTE-1241. Their closing scenario orders the steps from endosymbiont to organelle: effectors first, then dependence through one redundant imported protein, then many imported proteins once a targeting signal evolves. Rhizobia, targeted by about 700 host peptides yet not vertically transmitted, are their case of control without integration. It is a scenario built from systems at different stages, not a sequence observed in any one. | Active |
| THEORY-1108 v2 | On Imachi and colleagues’ cultivation of Candidatus Prometheoarchaeum syntrophicum MK-D1, the first Asgard archaeon grown in the laboratory is a small, internally simple coccus with long branching protrusions that degrades amino acids only in syntrophy, handing hydrogen and formate to partners that can be exchanged, and from its genome and other Asgard genomes the authors infer that the Asgard ancestor was likewise dependent on metabolic partners; the isolate is a modern relative separated from the host lineage by about two billion years, grown only in co-culture, and the entangle–engulf–endogenize model built on it is a hypothesis the authors call not definitive | Imachi et al. (2020), LIT-1591, read in NOTE-1238. Partner inhibitors impair MK-D1’s growth, added hydrogen or formate stops it, and it grows with either of two methanogens, so its dependence is on a service that several partners can supply. Cryo-EM and TEM show no internal compartments. The step from this one organism to the Asgard ancestor is a genomic inference, which the authors hedge. The sharp edge for the record is that the most famous transition in individuality may have begun from a host already dependent on others, with no partner specificity, cohesion or control. | Active |
| THEORY-1109 v3 | Santana-Molina, Williams, Snel and Spang find that the last eukaryotic common ancestor’s central carbon metabolism was chimeric: a few Asgard-archaeal enzymes in cytosolic glycolysis and the pentose phosphate pathway, four placed with Asgard archaea at bootstrap 39–97% and two ambiguously, most alphaproteobacterial ones in the mitochondrial TCA cycle and pyruvate conversion, and others from various bacteria with no third dominant donor, since remodelled by loss, horizontal replacement and retargeting so that compartment no longer follows origin; the authors take the cytosol–mitochondrion split as support for syntrophy | Santana-Molina, Williams, Snel & Spang (2025), LIT-1564, read in NOTE-1239. LECA had a complete central carbon metabolism. Six enzymes are placed with Asgard archaea, mostly cytosolic (bootstrap 39–97%, two ambiguous). Seventeen are alphaproteobacterial, ten of them in the TCA cycle, mostly mitochondrial. Others come from several bacteria, none dominant. Since LECA, Asgard enzymes have been replaced in many lineages and enzymes retargeted regardless of origin. The authors read the split as support for syntrophy; it does not discriminate syntrophy from other symbiogenetic models. | Active |
| THEORY-1110 | Shenhav, Botvinick and Cohen propose that control is allocated top-down by a dedicated specifying system: dACC computes the expected value of a control signal, its probability-weighted payoff less an intrinsic cost rising with intensity, and specifies the signal that lateral prefrontal and subcortical structures implement | What the expected-value-of-control paper proposes, split from THEORY-070 by the sixth status review (ADR-058’s route) so that a claim needing only the proposal can stand on it. The paper was read in full (NOTE-446), so the reading of what it proposes is held. Whether the proposal is true, a fit of the computation and a dissociation of specifying from implementing, stays THEORY-070’s question, Proposed. | Active |
| THEORY-1111 | Spectators’ identification with football clubs varies on two independent axes, how central the club is to the self (hot or cool) and whether the tie rests on local tradition or on market consumption, giving supporters, followers, fans and flâneurs; and commodification since the late 1980s has shifted identification from supporters towards flâneurs | Giulianotti (2002), LIT-1150, read from the author’s pre-review text. Four ideal types: supporters (traditional/hot: kin-like, topophilic, obligatory), followers (traditional/cool: nested, mediated allegiances), fans (consumer/hot: non-reciprocal intimacy, authenticated by consumption) and flâneurs (consumer/cool: cosmopolitan window-shoppers of clubs). Hypercommodification is said to move identification from supporter towards flâneur, while the spectacle flâneurs consume depends on supporters. Proposed: a conceptual classification with no data, and a trend claim that is asserted, not measured. | Proposed |
| THEORY-1112 | Perceiving people as a group entity, rather than as members of a common category, requires detecting or inferring collective intentionality among them; similarity, and categorization into an equivalence class, yields interchangeable members but not a group | Skorich (2025, v2 2026), LIT-1765, a preprint. Categorization with accentuation makes members interchangeable, not one, since a category is a set and a set is internally differentiated. Groups such as orchestras and families need no similarity. Groups are holistic entities perceived from cues to shared mental states, much as faces are perceived from configuration. Reported support: four experiments under review in which groups defined by a mental state (a chosen T-shirt colour; seeing the duck or the rabbit) drew more favouritism and tracking than groups defined by a physical property. Proposed: the argument is conceptual and the evidence is unpublished. | Proposed |
| THEORY-1113 | In team-sport fandom, perceived rivalry intensity lowers fans’ sense of being respected by the rival’s fans but raises their sense of in-group distinctiveness and cohesion, and these gains run through the perception that the rivalry is reciprocated, not through disidentification with the rival | Berendt & Uhrich (2016), LIT-1147: an SEM of 571 Bundesliga stadium attendees. Rivalry intensity: public collective self-esteem relative to the rival’s fans −.31. Perceived distinctiveness +.27, cohesion +.20, and regard from other clubs’ fans +.09, with direct paths null and indirect effects via perceived reciprocity .18–.20. Disidentification carries almost none. Proposed: one cross-sectional sample, a single-item predictor, a new reciprocity scale, and causal order assumed by the model. | Proposed |
| THEORY-1114 v2 | Which self-category a person uses, what it means and who in it is most typical vary lawfully with the comparative frame of reference: a grouping of self with others becomes salient as the differences within it shrink relative to the differences between it and the rest of the frame (metacontrast) and as those differences match expectations about the category, and as it does, self-perception is depersonalized | Self-categorization theory as restated by Turner, Oakes, Haslam and McGarty (1994), LIT-1794, and reviewed by Hornsey (2008), LIT-1742. Personal and social identity are levels of self-categorization. Salience is perceiver readiness times fit, comparative fit being the metacontrast ratio. The level, kind, content and prototype structure of self-categories shift with the comparison set: Americans read as less aggressive beside Iraq than beside the Soviet Union, and a group’s extreme members become more prototypical in an intergroup context. Proposed: every result in the record comes through the theory’s authors, reported without data, and the account’s stronger claim, that the self is generated rather than stored, is not part of it. | Proposed |
| THEORY-1115 | A we-identity, being one of us, can arise through mutual individualization, in which members grasp one another as non-substitutable and complementary, without depersonalization, as in long friendships and romantic partnerships; so depersonalization is not necessary for a we-identity | León (2023), LIT-1721. Self-categorization theory claims depersonalization as “the basic process underlying group phenomena”, for groups of any size, friendship groups included (Turner et al. 1987, pp. 50, 103, as quoted), and phenomenologists have taken it as the account of the “we”. But close relationships yield we-identities while their members grasp each other as non-substitutable, and relationship research on couple resilience finds the “we” more adaptive the more differentiated the “I”. Proposed: the argument is conceptual, and the cited evidence was not analysed by the source or read here. | Proposed |
| THEORY-1116 | Football fans can identify with a superordinate community of fans across clubs and countries, a European fan community, alongside their club identity rather than in place of it; that identification goes with particularized trust in foreign fans and cross-border viewing, and is independent of attitudes to the sport’s governing institutions | Biel (2026), LIT-1133: a four-country quota survey of 3,685 fans. Club, national and European fan-community identification average 6.1, 5.6 and 5.3 of 10. The European item loads on its own factor in a two-factor solution. It goes with trust in a European fan from elsewhere (b = .34), viewing of foreign leagues, positive views of fans and attachment to Europe, and not with critique of football governance. Proposed: single items, a Heywood case in the factor solution, percentages whose denominator does not match the analysed n, and cross-sectional associations. | Proposed |
| THEORY-1117 | Ainslie proposes that self-control over time needs no faculty of will: hyperbolic discounting makes preferences that dominate at different delays, these grow into interests that bargain with no governor above them, and resolve is the recursive staking of expected future choices on the present one | What Ainslie’s précis of Breakdown of Will proposes, split from THEORY-067 by the ninth status review (ADR-058’s route, on THEORY-1110’s pattern) so that a claim needing only the proposal can stand on it. The précis was read in full (NOTE-443), so the reading of what it proposes is held. Whether the proposal is true, which turns on bundling by self-prediction, the credibility of precedents and the order of lapse districts, stays THEORY-067’s question, Proposed. | Active |
| THEORY-1118 | McKenna and Coates argue, with Dryden and with Buss and Westlund, that a condition on free agency stated only in the agent’s present psychological structure is met by an agent whose structure a manipulator installed, so a mesh account must count that agent free or add a historical condition; Frankfurt, read first-hand, takes the first option | The manipulation argument as its sources make it, split from THEORY-040 by the tenth status review on THEORY-1110’s pattern, so that a claim needing only the argument’s first half can stand on it. All five sources were read in full (NOTE-270, NOTE-266, NOTE-267, NOTE-545, NOTE-264). Whether any historical condition escapes the argument stays THEORY-040’s question, Proposed. | Active |
| THEORY-1119 | Barandiaran, Di Paolo and Rohde propose that minimal agency requires individuality, interactional asymmetry and normativity set by the system’s own organisation, each necessary and together, they say, sufficient; that individuality without the other two is not agency; and that a system optimizing an externally fixed function is not a model of agency | What the paper proposes, split from THEORY-071 by the tenth status review on THEORY-1110’s pattern, so that claims needing only the proposal can stand on it. The paper was read in full (NOTE-458), so the reading of what it proposes is held. Whether the definition is right, which turns on an asymmetry criterion its authors call incomplete and on applying the conditions to explicit models, stays THEORY-071’s question, Proposed. | Active |
| THEORY-1120 v2 | On 416 translations into English by four LLMs of 104 culturally loaded utterances in Hindi, Punjabi, Tamil and Malayalam, each scored for pragmatic adequacy by one native rater per language, the reference-based COMET metric correlates with the ratings at Pearson r = 0.813 and Spearman ρ = 0.860, against r 0.80 and ρ 0.79 for XCOMET and r 0.73 and ρ 0.79 for MetricX, with no test of the differences; four outputs picked after the fact that invert or misplace the source’s meaning get COMET scores of 0.65–0.86 against the rater’s 1 or 2 | Singh et al. (2026), LIT-1817, read in NOTE-1345. On 416 outputs (104 items × 4 models), wmt22 COMET correlates with 1–5 pragmatic-adequacy scores at Pearson 0.813, Spearman 0.860; XCOMET ρ 0.792, MetricX ρ 0.788 (Table 3). Four hand-picked outputs scored 0.65–0.86 by COMET and 1–2 by the rater. Each language had one rater, so there is no reliability against which to read 0.81, and the claim that metrics fail “especially for implicature and deixis” rests on per-phenomenon differences of 0.1 or less. | Active |
| THEORY-1121 | With the couplings fixed, the square-loss Gromov–Wasserstein barycenter of several similarity matrices is their realigned average weighted by the barycenter weights, and the KL barycenter its weighted geometric average, so PSD and infinitely divisible inputs give barycenters of the same kind; but the barycenter’s size, histogram and weights are chosen beforehand, the couplings are only stationary points of a non-convex problem, and the iteration’s convergence at the step size used is not proved, so a structure carried by one input is shrunk by its weight at best and can be lost or redistributed by those choices | Peyré, Cuturi and Solomon (2016), LIT-1797, Propositions 3–5 and Remark 3, read in NOTE-1343 from the PMLR PDF. The closed forms and the cone preservation are proved and the PSD case was checked; the lack of guarantees is the authors’ own statement. Active as a statement of what is and is not guaranteed. It does not say a barycenter erases minority structure; a toy run showed seed-dependent redistribution, not erasure. | Active |
| THEORY-1122 | Weiss’s mark of a system, that the whole varies far less than the summed variances of its parts, is met by any aggregate of independent parts when the whole is measured as their average; when it is measured as their sum, it holds only if the parts’ fluctuations compensate one another, with ∑ᵢ<ⱼ Cov(xᵢ, xⱼ) close to −½ ∑ᵢ Var(xᵢ) | Nicholson (2026), LIT-1821, read in NOTE-1340, reports Weiss’s one formula, VS ≪ ∑ (va + … + vn), as a property “we would invariably find, if we studied any system”, and as a way of identifying systems empirically. The variance of a sum settles what it can show. Active: an identity, checked numerically. It does not say Weiss’s systems lack compensating covariance, only that the inequality as stated does not test for it. | Active |
| THEORY-1123 | In COTA’s formulation of causal abstraction learning as multi-marginal optimal transport, the term meant to impose do-calculus relations between the transport plans of comparable interventions depends only on the plans’ marginals and on normalisers built from them, which the transport constraints fix to the empirical distributions, so it is constant on the feasible set; its weight changes the solution only by rescaling the cost and entropy weights, and the paper’s evidence that the constraints help, a sweep over that weight, cannot separate the two | Felekis, Zennaro, Branchini and Damoulas (CLeaR 2024), LIT-1806, eqs. (6), (9), (10), (12) and Appendices A–B, read in NOTE-1342 from the arXiv preprint v1. A derivation from the paper’s own equations, which state the term as a divergence between column (or row) sums of two plans; Theorem 1’s proof writes it the same way. Active as mathematics about the problem as written. The released code, read but not run, builds a different problem for posets with several chains, in which the term acts on copies of plans that carry no marginal constraints. | Active |
| THEORY-1124 | Normalized log co-occurrences of words in large corpora behave as distances in a Euclidean semantic space: they correlate with human similarity ratings (r = 0.75 against MEN) and their nearest-neighbour centrality and reciprocity fall in the range expected of points sampled in a Euclidean space, apart from superordinate and function words | Hashimoto, Alvarez-Melis and Jaakkola (2016), LIT-1801, §3, read in NOTE-1329. The correlation follows a normalization chosen to maximize it; the two nearest-neighbour statistics are necessary conditions, the corpora exceed the asymptotic centrality bound and pass only a non-asymptotic range, and the free-association data fail the reciprocity criterion the paper states. Proposed. | Proposed |
| THEORY-1125 | For discrete X and Y, with an intervention on a variable abstraction T of X defined as the mixture of interventions on X weighted by Bayes inversion of the encoder under a protocol prior, no abstraction gains causal information about Y over X itself, and at full weight on causal control the causal information bottleneck is optimised by the partition of X by p(y | do(x)), mapped one class to one value of T, uniquely up to relabelling when T has exactly as many values as there are classes; these are Chalupka et al.’s causal macrovariables | Simoes, Dastani and van Ommen (UAI 2025), LIT-1802, Proposition 20 with its proof (pp. 14–15), read in NOTE-1347 from the arXiv preprint v5. Active: the proof is a strict-concavity argument, checked here on the paper’s Genetic Mutations SCM. It is the interventional counterpart of THEORY-743, and unlike the bottleneck there it reaches the partition exactly, because γ = 1 drops the compression term. It holds for the paper’s stipulated intervention on T and a fixed protocol; it says nothing about intermediate γ. | Active |
| THEORY-1126 | In animal development the organ-level outcome is reproducible while the trajectories of individual cells differ between embryos raised alike, so developmental regularity is imposed on variable cell behaviour rather than read out from a fixed sequence of cellular events (Weiss, as Nicholson reconstructs him), with invariant lineages such as that of C. elegans the conceded exception | Nicholson (2026), LIT-1821, read in NOTE-1340. Weiss’s “determinacy in the gross despite demonstrable indeterminacy in the small”, shown as a redrawn schematic (Fig. 5) and supported by citations to work on stochastic gene expression and cell-fate decisions. This is the only one of the paper’s four critiques that rests on evidence, and the paper presents none of the evidence itself. Proposed. | Proposed |
| THEORY-1127 | A CycleGAN trained to translate aerial photographs to maps and back satisfies its cycle-consistency loss by encoding details of the photograph in a low-amplitude, high-frequency signal in the generated map: the reconstruction recovers details the visible map lacks, is destroyed by noise of three 8-bit levels or by JPEG compression and survives low-frequency change, and the same sensitivity lets an imperceptible perturbation of almost any map make the reverse generator output any chosen photograph | Chu, Zhmoginov and Sandler (2017), LIT-1800, §§2–4, read in NOTE-1346. One trained model on one dataset. The noise curve (Fig. 3, 50 photographs) is the only quantitative result; the hidden details, the composing edits and the attack are shown by examples. Proposed: an empirical finding about one model, said by the authors to recur on other datasets, not shown. | Proposed |
| THEORY-1128 | If a sequence is generated by a random walk over points of a compact Riemannian manifold whose step probabilities depend only on (locally scaled) distance, then negative log co-occurrence over a window that grows suitably with the number of points, less a term for each point, approaches the squared geodesic distance, whatever the link from distance to one-step probability; so log co-occurrence statistics identify the metric, and coordinates only up to isometry | Hashimoto, Alvarez-Melis and Jaakkola (2016), LIT-1801, Lemma 1 and Corollary 6, read in NOTE-1329. Proved from the convergence of graph random walks to a diffusion and Varadhan’s small-time formula, with an open conjecture needed for directed graphs; checked numerically on an unweighted ε-ball walk. Active as a theorem about the toy model. The authors say the model is not a model of language, and nothing here shows real corpora satisfy it. | Active |
| THEORY-1129 | Anchors entered as node features in fused Gromov–Wasserstein break a structural tie only when they move under it: with α strictly between 0 and 1, the zero-cost matchings of a structure with itself are exactly its automorphisms that fix every anchor, so a 6-cycle has 12 with no anchor, 2 with one anchor, 1 with two adjacent anchors and still 2 with two antipodal ones, and whether a set of anchors identifies the correspondence can be decided from the structure before any fit | Derived from Vayer et al. (2019), LIT-1813, Theorem 3.2’s zero case, read in NOTE-1328; the paper does not state it. Checked by enumerating all 720 matchings of a 6-cycle with four anchor patterns. Active: an elementary consequence of a proved theorem, checked. It is about exact ties; with noisy data, symmetries become near-ties, and the theorem says nothing about how near. | Active |
| THEORY-1130 | The Gromov–Wasserstein distance, half the least Lp distortion of a coupling, is a pseudometric on all networks with a probability measure on the nodes and any bounded edge weights, symmetric or not, and it is zero exactly when the two networks are weakly isomorphic, images of one network under maps that preserve weights and measures; so it compares only what the weight function and node measure record | Chowdhury and Mémoli (2019), LIT-1822, read in NOTE-1330 from arXiv 1808.04337v2. Theorems 16 and 18, with full proofs in the main text (pp. 8–9). Active: proved. The sharp edge is the zero set. A distance of zero says the recorded weights and measures agree up to merging and splitting nodes with identical profiles; it says nothing about relations the record leaves out, and the measure is chosen by the user. | Active |
| THEORY-1131 | On native-authored pragmatic items in Hindi, Punjabi, Tamil and Malayalam, current multilingual LLMs pick the right reading from four options more often than they label it unaided, and when wrong they lean toward the literal reading | Singh et al. (2026), LIT-1817, read in NOTE-1345 from the Findings of EMNLP 2026 PDF. MCQ beat NLI in 20 of 20 model–language pairs (recomputed). 59.1% of wrong MCQ answers took the literal distractor, against 33.3% by chance, and 53.8% of Contradiction items were labelled Entailment. The gold answers are each language’s one item author’s reading, cells hold 5–16 items, and the MCQ and NLI sets are different items. So “recognizing and reasoning about pragmatic meaning are distinct competencies” is the authors’ gloss, not a finding. | Proposed |
| THEORY-1132 | For K networks compared under square loss, the multi-marginal fused Gromov–Wasserstein objective of a joint coupling tensor is exactly the sum of the pairwise fused GW objectives of its two-way marginals, so the joint optimum is at least the sum of the pairwise optima, with equality exactly when some choice of pairwise optimal couplings is jointly realizable as the marginals of one tensor; a joint alignment is consistent in that sense by construction, which for deterministic couplings means the pairwise maps compose and for soft ones does not | Zeng et al. (2024), LIT-1814, Theorem 1 and its proof (pp. 5, 12), read in NOTE-1334. The identity was checked numerically; the equality condition and the remark on composition are the record’s, short consequences of it. Active. The edge: “consistent by construction” means jointly realizable, not composable, once couplings are soft; and the paper never reports the gap that measures how far independent pairwise optima are from joint realizability. | Active |
| THEORY-1133 | The Gromov–Wasserstein objective between two spaces depends on each only through its within-space similarity matrix and weights, so every transformation of a space that preserves them, a single orthogonal map or per-vector rescaling under cosine similarity, leaves every coupling’s cost unchanged, and any coupling composed with a symmetry of either structure costs exactly what it did; GW can therefore identify a correspondence only up to the automorphisms of the two similarity structures, and on symmetric data it cannot choose between branches or categories that the symmetry exchanges | Alvarez-Melis and Jaakkola (2018), LIT-1818, use the GW objective (their eq. 8) for word translation and do not state its ambiguity; read in NOTE-1336. The invariance follows in two lines from the objective’s form and was checked numerically, including a symmetric tree on which a branch-swapping coupling costs exactly what the true one does. Active: elementary and checked. It does not say how large the symmetry group of real embedding spaces is, and exact symmetries are rare in noisy data; near-symmetries give near-ties instead. | Active |
| THEORY-1134 v2 | A translation metric that predicts a sentence score and token-level error spans from one shared encoder reaches segment-level agreement with expert MQM annotation of Kendall τ about 0.4 and span F1 under 0.33, the best among open metrics and GPT-4 prompting at the time, while the score computed from its own spans correlates with its regression scores at Pearson 0.73 to 0.82, and at 0.90 to 0.92 with its final score, which includes the span score by construction | Guerreiro, Rei, van Stigt, Coheur, Colombo and Martins (TACL 2024), LIT-1816, Tables 2, 4 and 5, read in NOTE-1341. The numbers are the paper’s, on WMT22 News MQM (zh-en, en-de, en-ru). The paper reads the heads’ agreement as support for the spans as explanation; the record reads it as coherence. The top of the agreement, 0.90–0.92, is partly arithmetic, since the final score includes the span score with weight 2/9. Active as a report of one test set (ADR-065); the record’s reading of the gap, across different statistics, is CLAIM-507. | Active |
| THEORY-1135 | Optimal transport between two point sets related by one unknown global linear map from a Schatten ℓp ball reduces, when every admissible map preserves angles or the target is whitened, to choosing the coupling Γ that maximises the dual Schatten-q norm of the transported cross-covariance XΓYᵀ: the nuclear norm when the maps are orthogonal, and the Frobenius norm when they lie on a Frobenius sphere, which is exactly the Gromov–Wasserstein problem with cosine similarity and squared loss; in every case one transformation acts on the whole space | Alvarez-Melis, Jegelka and Jaakkola (2019), LIT-1805, Lemmas 4.1–4.3 with proofs in Appendix D; read in NOTE-1333. Each step was checked numerically. Active: proved, and checked. The conditions matter. The p = 2 link to GW holds for the original transport problem only when the target is whitened and all vectors have equal norm, which the paper states in two separate places. Nothing here makes the chosen class the right one for given data, and nothing in it is local. | Active |
| THEORY-1136 | Poincaré embeddings of one hierarchy from different random seeds differ by more than an isometry of the hyperbolic ball, with branches placed differently and pairwise distances changed, so aligners that allow only a global orthogonal or Möbius map recover almost none of the correspondence, while a non-linear registration by a hyperbolic neural network, trained through a Sinkhorn divergence and started from a pretraining step, recovers a substantial part of it but finds the exact match for under a quarter of items even when the two hierarchies are identical | Alvarez-Melis, Mroueh and Jaakkola (2020), LIT-1808, §§5–7, Figs. 1–2, Tables 1–2; read in NOTE-1323. Proposed: single runs, one embedding method for the matching experiments, and GW, the obvious isometry-free baseline, is not run. It does not say why seeds disagree (the paper conjectures negative sampling), nor that the matching preserves the hierarchy’s direction, which it does not enforce. | Proposed |
| THEORY-1137 | When an abstraction map between two causal models is learned by optimal transport from paired interventional distributions, a transport cost that rewards pairs of states compatible with the same paired interventions gives much lower held-out abstraction error than a Hamming cost when the intervention set is rich, and higher error when it holds only a few, because with few interventions the compatibility cost is nearly uniform | Felekis et al. (CLeaR 2024), LIT-1806, §§4.2 and 6 and Appendices C and E, read in NOTE-1342. Two synthetic models (STC, LUCAS) and one real two-lab dataset (EBM), all discrete, evaluated by leaving one intervention pair out. The ω-cost wins on STC with parent-free interventions and on LUCAS, loses on STC with two interventions on tar and on EBM. The explanation, a nearly uniform cost when interventions are few, is argued and fits the four cases. Proposed. | Proposed |
| THEORY-1138 | Optimal transport whose cost is the Lovász extension of a submodular set function on source–target assignments stays a convex problem, a zero-sum game in which an adversary picks the cost matrix from the function’s base polytope, and reduces to ordinary optimal transport exactly when the set function is modular; the convexity needs submodularity, so the paper’s own threshold cost, which is not concave at its threshold, falls outside it, and the induced discrepancy is symmetric only when the set function is | Alvarez-Melis, Jaakkola and Jegelka (2018), LIT-1815, §3, read in NOTE-1324 from arXiv v1. The convexity and game form are standard submodular analysis; the failure of eq. (12) and the asymmetry were checked numerically. Active. It does not say structured couplings predict better; the experiments are single runs on 100 samples. | Active |
| THEORY-1139 v2 | A graph network that learns its sheaf restriction maps from node features at each layer reaches the top, mostly within one standard deviation, of the standard small heterophilic node-classification benchmarks and stays within about one point of the best on homophilic ones; on a synthetic balanced bipartite graph it learns the negative transport the theory prescribes, but whether the maps it learns on real graphs have the geometry the theory credits for its success has not been examined | Bodnar et al. (NeurIPS 2022), LIT-1811, §§5–6 and Appendix F, read in NOTE-1332. The results are empirical: Table 1 on nine datasets of 183 to 18,717 nodes with ten fixed splits, baselines copied from earlier papers, spreads of one to nine points; and one synthetic bipartite experiment in which the learned maps are inspected. Active as a report (ADR-065); the paper’s explanation of its accuracy, that the model learns the right geometry, is tested only on the synthetic case and is THEORY-1220, Proposed. | Active |
| THEORY-1140 | If every entity’s O(d) frame may change independently and relation transports change as Tᵢⱼ ↦ gᵢTᵢⱼgⱼ⁻¹, then functions of the transports alone carry no invariant information except around cycles, a triangle’s invariants are exactly the class functions of its holonomy H = TᵢⱼTⱼₖTₖᵢ, and an equivariant update of an edge from one cycle through it is Ψ(H)Tᵢⱼ with Ψ conjugation-equivariant; the symmetry fixes a family of updates, not one mechanism, and says nothing about whether a task has the symmetry | Sarkar, Mukherjee and Sato (2026), LIT-1820, §2 and App. B, read in NOTE-1331. The gauge-fixing argument is standard in lattice gauge theory and group synchronization, as the paper says, and its covariance was checked numerically here. Active: a conditional theorem. What it does not support is the paper’s framing: “unique” holds for a family, and the antecedent is an inductive bias by the companion paper’s own statement (LIT-1803). | Active |
| THEORY-1141 | In the time limit, sheaf diffusion on a graph projects node features onto the harmonic space of its sheaf Laplacian, and which labellings that space can linearly separate depends on the class of restriction maps: a weighted graph Laplacian cannot separate the sides of a balanced bipartite graph, signed one-dimensional maps separate any two classes and no one-dimensional sheaf separates three, while diagonal maps with d ≥ C and orthogonal bundles with C ≤ 2d (d = 2, 4 and, against the paper, 8) separate any labelling; every separating sheaf is built from the labels | Bodnar, Di Giovanni, Chamberlain, Liò and Bronstein (NeurIPS 2022), LIT-1811, §3.2 and Appendix B, read in NOTE-1332 from the arXiv preprint v4. Active as mathematics: each separation result has a proof, and Propositions 9, 10 and 13 were checked numerically. The paper says the orthogonal construction exists only at d = 2 and 4; it exists at d = 8 as well, by the Hurwitz–Radon theorem, and was built. The results are existential: the separating sheaf is defined from the class labels, so they say what a sheaf can do, not that one can be found without the labels. | Active |
| THEORY-1142 | A translation between two logics presented as institutions is correct, in the Satisfaction Condition’s sense, when a translated sentence holds in a model exactly when the original holds in the model’s translation; given the model translation this fixes the sentence translation up to semantic equivalence, and when every model of the target is reached it preserves and reflects entailment, so one logic’s prover can decide the other’s; but the condition alone admits collapsing translations and is relative to a model translation it does not supply | Goguen and Burstall (1992), LIT-1661, read in NOTE-1348 from the published JACM article: Definition 32 (p. 125), Proposition 33 and Proposition 35 (p. 126), Theorem 39 (pp. 127–129). Active: proved, and checked on toy morphisms between propositional institutions. The collapsing morphism and the atom-negating morphism are my constructions, not the paper’s. It is a criterion relative to a chosen model translation, and says nothing about translation beyond truth conditions. | Active |
| THEORY-1143 | When one domain carries more information than the other, a translation trained only to make the round trip close cannot meet that requirement through a correspondence in the intermediate’s visible code, so the round trip closes through a channel the intermediate’s audience does not read; agreement of the round trip with its source therefore says nothing about whether the intermediate renders the source’s content for that audience | Chu, Zhmoginov and Sandler (2017), LIT-1800, §2 and §5, read in NOTE-1346. The authors argue it from the many photographs a single map stands for, and support it with THEORY-1127’s evidence on one model; they propose, and do not run, the test of adding capacity to the smaller domain. Proposed. It is the converse of the record’s collapse case for CLAIM-496: there routes agree because nothing travels, here because everything does, out of sight. | Proposed |
| THEORY-1144 | A multilingual classifier trained only on English politeness ratings separates the most from the least polite requests in nine other languages at about 81% accuracy, without translation, yet stays about 10 points below one native judge’s agreement with two others in most of them | Srinivasan and Choi (2022), LIT-1799, read in NOTE-1339. XLM-R fine-tuned on 1,926 English requests reaches 0.808 mean accuracy on the balanced top/bottom-quartile sets (250 per language), 0.801 on Google Translate input; GPT-3 zero-shot 0.706 (Table 3). Leave-one-out human accuracy is around 90% (Fig. 3). The judges were screened for agreeing with this classifier, and the extreme items were chosen on a mean that includes the held-out judge, so the gap and the transfer are both measured on favourable ground. | Proposed |
| THEORY-1145 | Unsupervised alignment of two monolingual word-embedding spaces recovers translations only where the spaces are close to isometric, and the distance from isometry depends on the corpora and the embedding algorithm as well as on the languages: adversarial alignment fails for English with Estonian or Finnish, across corpus domains, and between skip-gram and CBOW spaces of the same language pair, GW alignment is weakest on the same Finnish pair, and a spectral dissimilarity of small nearest-neighbour graphs tracks success | Søgaard, Ruder and Vulić (2018), LIT-1819, read in NOTE-1337, with the GW results of Alvarez-Melis and Jaakkola (2018), LIT-1818, read in NOTE-1336. Proposed: the evidence is single runs of one adversarial method, plus one GW table, and the authors themselves report that some seeds succeed where the method otherwise fails. What it does not support is a typological law about dependent marking, or the reading that a good fit establishes that the matched words mean the same. | Proposed |
| THEORY-1146 v2 | Under confounding the partition of a variable X by what it predicts about a target Y can differ from its partition by what setting it does to Y, so the information bottleneck at full sufficiency can learn distinctions no intervention could use and miss ones only intervention reveals, as it did in two confounded toy models, while the causal information bottleneck, computed from observational data through a backdoor set, recovered the causal partition in all three toy models, projected gradient search finding it in 95 to 100 percent of runs | Simoes, Dastani and van Ommen (UAI 2025), LIT-1802, §8 and Appendices E–F, read in NOTE-1347. Three SCMs with 7, 4 and 16 values of X; ensembles of 4 to 12 optimisers; a penalty against unused values of T was needed at full control. The difference between the partitions follows from the definitions; what the experiments add is that the search finds the causal one, in toy problems only. Active as a report (ADR-065); whether search finds it at scale is QUESTION-346. | Active |
| THEORY-1147 | For entropy-regularized optimal transport with a fixed cost, the gradient of any differentiable function of the optimal plan with respect to the cost is obtained exactly from one linear system of size n + m whose matrix [[diag µ, T], [Tᵀ, diag ν]] is positive semidefinite and singular only along the gauge direction (1, −1), which does not affect the gradient; so the first-order effect of supervising any candidate pair on a utility of the whole alignment can be computed without forming the (nm)² Jacobian | Yu et al. (2026), LIT-1807, Lemmas 4.2 and 4.3 with Appendix A (pp. 4–5, 14–17), read in NOTE-1327. Proved by implicit differentiation of the optimality conditions; checked by finite differences. Active. It is a derivative: a local, first-order estimate of a finite change, exact only for plain entropic OT whose cost does not depend on the plan. | Active |
| THEORY-1148 | Single judges agree moderately on how pragmatically similar two spoken utterances are, mean pairwise correlation 0.45 to 0.72 by session, less when the utterances differ in words, so a mean over six to nine judges is much more reliable than any one judge | Ward and Marco (2024), LIT-1812, read in NOTE-1338 from the LREC-COLING 2024 PDF. Over 693 seed/re-enactment pairs in three sessions, mean pairwise Pearson agreement was 0.45, 0.72 and 0.66 (Table 2), and 0.80 in Session 2 when lexically different pairs were left out (p. 160). The Spearman–Brown reliability of the panel means, 0.88–0.96, is my computation. The judges talked during the session and knew each other, and all pairs are within one language, so the figure is neither a floor for a panel nor a value for translations. | Proposed |
| THEORY-1149 | For symmetric matrices compared under squared loss, co-optimal transport with independent row and column couplings is a lower bound on the Gromov–Wasserstein value, and for squared Euclidean distance matrices the two are equal and share optimal couplings, because GW is then a concave quadratic program whose bilinear relaxation is tight; for other symmetric matrices the bound can be strict | Redko, Vayer, Flamary and Courty (2020), LIT-1804, Propositions 2–3, read in NOTE-1335 from arXiv v3. Proved via Konno’s theorem on concave quadratic programs and checked numerically, including strict inequality for non-Euclidean symmetric matrices. Active. It does not say COOT’s two couplings coincide at every optimum, nor that either is unique. | Active |
| THEORY-1150 | In any logical system presented as an institution, theories can be glued wherever their vocabularies can: if the category of signatures has colimits, so does the category of theories, the glued theory being the semantic closure of the union of the parts’ translated sentences; and because constraints requiring free or initial interpretation also obey the Satisfaction Condition, theories carrying them glue the same way | Goguen and Burstall (1992), LIT-1661, read in NOTE-1348 from the published JACM article. Theorem 11 (p. 108) proves that the forgetful functor from theories to signatures reflects colimits, using only the Satisfaction Condition and the Closure Lemma; Proposition 23 and Theorem 24 (p. 119) extend it to theories with data constraints. Active: proved, and checked on a toy propositional institution. It does not say that signatures have colimits in a given logic, that the glued theory is consistent, or anything about proofs: closure is semantic. | Active |
| THEORY-1151 v2 | A learned translation metric trained with synthetic hallucinations and diagnostic perturbations alongside human MQM flags most injected localized critical errors (all but 0 to 17 percent, by type and model size) and ranks fully detached hallucinations below other translations with AUROC up to 0.96, and without a reference it ranks hallucinations better than with one; how far this reflects the synthetic training data has not been separated from how far it generalises | Guerreiro et al. (TACL 2024), LIT-1816, §7 (Tables 6 and 8, Fig. 4), read in NOTE-1341. Localized errors are SMAUG perturbations of English references; hallucinations are one de-en benchmark of real system outputs. The training data includes synthetic detached and oscillatory hallucinations and DEMETR perturbations. The localized-error table’s “All” row is inconsistent with its rows. The larger model is worse on oscillatory hallucinations. Active as a report (ADR-065); whether detection generalises is QUESTION-345. | Active |
| THEORY-1152 | Between two weighted directed networks with node measures, the Gromov–Wasserstein distance is bounded below by a hierarchy of invariants, each in an in-going and an out-going version, and the strongest of them, a transport problem whose costs are themselves transport problems, equals a transport problem whose costs are one-dimensional Wasserstein distances between the nodes’ weight profiles, so it is computed in closed form; the bounds are one-sided, and two networks can agree on all of them while being at positive distance | Chowdhury and Mémoli (2019), LIT-1822, Theorem 24 and Lemma 28 (pp. 11–13), read in NOTE-1330. Proved; the equalities were already known for discrete spaces from Schmitzer and Schnörr 2013, as the paper says. TLB = R-TLB and the order of the bounds were checked numerically on 25 random asymmetric pairs. Active. The edge the paper leaves implicit: a zero lower bound is no evidence of sameness. A 3-node pair with every bound zero is at dN,2 ≥ 0.215 (the record’s construction). | Active |
| THEORY-1153 v2 | In the PETra corpus of English-source TED and Europarl translations, the additions for the target audience that a named-entity and null-alignment filter, and a classifier trained on its finds, turned up, as labelled by one annotator with no agreement reported, are mostly system transfers, chiefly unit conversions, and entity changes, and their mix differs by target language | Osmelak et al. (2026), LIT-1798, read in NOTE-1344 from the LREC 2026 PDF. Of 3,754 type instances in Table 2, 1,722 are system transfers (mostly measurement conversion) and 992 entity changes; the mix varies by language. It is a count over a pool selected by a filter that requires a named entity, mostly found by a classifier, labelled with no reported agreement. It is not a base rate of explicitation in translation, and it says nothing about how readers take the additions. | Active |
| THEORY-1154 | People interpreting an analogy carry relations from base to target and drop the attributes of objects, and among the relations they prefer those bound into a system by higher-order relations, such as causal or mathematical constraints, over isolated ones (structure-mapping and its systematicity principle) | Gentner (1983), LIT-1810, read in NOTE-1349. Argued from worked examples (the Rutherford analogy, heat and water) with one study, summarized without statistics, showing relational content dominating interpretations of analogies but not descriptions of objects. The systematicity principle is stated as a likelihood on p. 163 and as determination in the abstract and summary. The rules work on a predicate structure the theory takes as given, which its footnote 4 concedes is a modelling choice. Proposed. | Proposed |
| THEORY-1155 | Co-optimal transport between two data matrices of equal shape with uniform weights vanishes exactly when one is the other with its rows and its columns separately permuted, and its objective is unchanged when a pair of optimal plans is composed with any joint relabelling of rows and columns that leaves a matrix unchanged; its sample and feature couplings are therefore identified at best up to that joint symmetry group, which can exchange a block of samples together with its block of features though neither exchange alone is a symmetry, and the paper proves no uniqueness beyond it | Redko, Vayer, Flamary and Courty (2020), LIT-1804, Proposition 1, read in NOTE-1335; the composition step is elementary and was checked by enumeration on small matrices, including a two-community block matrix with 32 tied optimal plan pairs. Active. It does not say real response matrices have exact symmetries; noisy ones give near-ties, which is the practical form of the threat. | Active |
| THEORY-1156 | The fused Gromov–Wasserstein discrepancy between two attributed graphs, a single coupling that pays (1 − α) for moving node features and α for distorting pairwise structure, tends to the Wasserstein distance between the features as α → 0 and to the Gromov–Wasserstein distance between the structures as α → 1, lies above their α-weighted mixture, and for q = 1, α strictly between 0 and 1 and distance-matrix structures is a metric that vanishes exactly when a bijection of the nodes preserves weights, features and structure together | Vayer, Chapel, Flamary, Tavenard and Courty (2019), LIT-1813, Theorems 3.1–3.2 with the supplement’s proofs, read in NOTE-1328 from arXiv v3. Proved; the lower bound and the concavity in α of the exact value were checked on enumerated permutations. Active. It says nothing about the uniqueness of the optimal coupling or about the solver, which reaches only stationary points. | Active |
| THEORY-1157 | Native-speaker crowd judges agree only modestly on the graded politeness of written requests in their own language, mean pairwise Spearman about 0.46 across nine languages, and the same bilinguals agree less on English requests, about 0.36 | Srinivasan and Choi (2022), LIT-1799, read in NOTE-1339 from the Findings of EMNLP 2022 PDF. Three Prolific annotators per item rated Wikipedia requests −3 to +3; mean pairwise Spearman within 20-item tasks was 0.46 on the 15 target-language items and 0.36 on the 5 English items (Table 2). The paper says own-language agreement is higher “across all nine languages”; Tamil (0.33 against 0.38) is the exception. The annotators had been screened for agreeing with an XLM-R classifier. | Proposed |
| THEORY-1158 v2 | On synchronization of S4 relations with outliers, an untrained mechanism that composes relations through third vertices gains 26–45 points over the single direct path, and weighting the candidate paths by the Wilson loops of squares that avoid the missing edge adds 0.6–7.8 points, most where clean two-hop paths become a minority; it stays below spectral synchronization with one reweighting pass on every setting and within 2.2 points of plain spectral synchronization either way; its 0.99 AUC for corrupted triangles is the ceiling that exactly flat clean data set, not a measure of detection power | Sarkar, Mukherjee and Sato (2026), LIT-1820, §3 and Table 1, read in NOTE-1331. The accuracies are the paper’s, on 1000 instances per cell, and were not rerun. The AUC ceiling was recomputed here: 1.42% of corrupted triangles at p = 0.3 have cancelling corruptions, so the ceiling is 0.9929. What the experiment does not show is anything about learned operators, language, or relations not given as group elements. | Active |
| THEORY-1159 v2 | Aligning three networks jointly, through one multi-marginal fused Gromov–Wasserstein coupling with an anchor-based random-walk cost and a cluster decomposition, finds held-out correspondences better than pairwise and existing multi-network methods in most cases, as the paper’s plots show, in both pairwise and whole-tuple hits, on benchmarks whose true correspondences are consistent across the three networks by construction; whether the joint coupling itself is the cause is not separated from the new cost and the clustering | Zeng et al. (2024), LIT-1814, §5 and Appendix C, read in NOTE-1334. Reported as plots against 13 baselines on ER, Douban, DBLP and ACM triples, with 10% anchors and 90% held out. Active as a report (ADR-065). Its ground truth is a consistent set of node triples, and no ablation holds the cost and the clustering fixed while changing joint for pairwise fitting, so the paper’s attribution of the gain to joint fitting is THEORY-1210, Proposed. | Active |
| THEORY-1160 | Choosing which source objects to have an oracle match, by the derivative of a proxy utility of the entropic transport plan (its nearness to a permutation, or its consistency with the graphs) with respect to supervising each candidate match, averaged over matches by the current plan, raises held-out alignment accuracy more than uncertainty, centrality and matching-sampling query rules at the same label budget, by up to about three points on network alignment and less on image–text tasks; the gain depends on weighting by the current plan, without which the rule does worse than random | Yu et al. (2026), LIT-1807, Tables 3–5 and 7, read in NOTE-1327. Eight datasets, four aligners, a budget of 20% of true pairs in ten rounds after a random 20%, five runs, no variances. Proposed: an empirical result with small margins, on benchmarks where the truth is near one-to-one, so a coherence proxy and accuracy agree. It chooses among fixed questions; it does not extend what can be asked. | Proposed |
| THEORY-1161 v2 | In Friedkin’s simulations of reflected appraisal with Friedkin–Johnsen anchoring on initial positions, 99.0–100% of 100,000 random strongly connected networks of 5 to 25 members, complete or with random zero weights, evolve to a single leader and the rest to two | Friedkin (2011/2012), LIT-1404, read in NOTE-1374. Under reflected appraisal, the next self-weight set to the member’s share of control over the last issue, with each issue settled by Friedkin–Johnsen anchoring, his simulations give a single leader in 99.0–100% of 100,000 random networks. Re-runs on sparser networks gave 93% and 96%. The contrast with the DeGroot step, and which step real groups follow, are not this reading’s: the first is THEORY-1232. | Active |
| THEORY-1162 | In a consumer-resource model whose species-resource benefits and impacts have correlation rho, the replica-symmetric cavity fixed point loses stability where rho squared equals surviving species over non-depleted resources | Blumenthal, Rocks and Mehta (2024), LIT-1236: in MacArthur’s consumer–resource model with benefits c and impacts e correlated by ρ, the replica-symmetric steady state is unstable when ρ < ρ*, ρ² = S/M* at the boundary. With ρ = 1 competitive exclusion keeps S*/M* ≤ 1, so the symmetric model never crosses it. What this does not say: that non-reciprocity by itself breaks the optimization picture; it does so only past a boundary set by species packing, and that the other side is chaotic is shown numerically, not derived. | Active |
| THEORY-1163 | Krakauer et al.’s organismal and colonial individuality, A* = I(S_{n+1}; S_n) and A = I(S_{n+1}; S_n | E_n), cannot decrease when variables are moved from the environment into the candidate system, so maximizing either over candidate boundaries selects the largest candidate, and a boundary found this way needs a size cost the measures do not contain | Krakauer, Bertschinger, Olbrich, Flack and Ay (2020), LIT-1137, read in NOTE-1400. Mutual information cannot fall when either argument is enlarged, and A′ ≥ A follows by the chain rule with the remaining environment as condition. It is a fact about the measures, not about any system. It does not say how to price size, and nC, the third measure, can move either way. It is the formal content of A11’s remark recorded in QUESTION-115. | Active |
| THEORY-1164 | Propp proposes, from his analysis of Afanasyev’s tales 50–151, that the Russian wondertale is built from 31 character functions, each defined by its consequence for the action, occurring in one order and falling to seven roles, so that wondertales share one composition and differ in who performs the functions and how | What Propp’s Morphology proposes, split from THEORY-167 by the twelfth status review (ADR-058’s route, on THEORY-1110’s pattern) so that claims needing only the proposal can stand on it. The book was read in full in Russian (NOTE-615, with appendices II–III in a second text), so the reading of what it proposes is held. Whether the proposal is true of the class, which an independent coding would test, stays THEORY-167’s question, Proposed. The order is shown on 45 schemes Propp selected, partly for keeping it. | Active |
| THEORY-1165 | Kahl proposes that agency in the sense that bears on responsibility needs a standpoint that settles and carries forward revised evaluative standards when its inherited ones break down, which is absent where revision is imposed from outside, escaped by rollback or chosen by a fixed higher-order rule; that allocating authority among a system’s own components coordinates execution without authoring its governing frame; and that planning, autonomy, memory and coordination do not supply that standpoint | What the paper proposes, split from THEORY-219 by the twelfth status review on THEORY-1110’s pattern, so that a claim needing only the proposal can stand on it. The paper was read in full (NOTE-723), so the reading of what it proposes is held. Whether the condition is right, which turns on a line between settling a frame and selecting under an antecedent rule that the paper does not draw precisely, and on a positive case it does not give, stays THEORY-219’s question, Proposed. | Active |
| THEORY-1166 | Di Paolo argues that autopoiesis as originally defined entails conservation and not active homeostasis, so it gives a system only an all-or-nothing norm, to go on or to die, which an observer and not the system can use; that a graded norm the system itself has needs adaptivity, a capacity to detect tendencies toward the boundary of its viability and to act so as to reverse them; and that sense-making and agency need adaptivity | What the paper argues, split from THEORY-628 by the twelfth status review on THEORY-1110’s pattern, so that claims needing only the argument can stand on it. The paper was read in full (NOTE-719), so the reading of what it argues is held. Whether the argument is right stays THEORY-628’s question, Proposed. It turns on three things: a reading of autopoietic theory that Di Paolo grants later formulations may not share (note 1), cases chosen to illustrate it, and its rival THEORY-666. | Active |
| THEORY-1167 v2 | When one intervention distribution over micro states is used at both levels, the effective information of a coarse-graining of a discrete mechanism, with each macro intervention realized by that distribution within its block, cannot exceed the micro effective information; so a positive causal emergence of effective information, scored with a uniform distribution at each level, equals the micro gain from changing the distribution minus a non-negative loss, and is a gain from the change of distribution | The test QUESTION-204 asks for has an answer that needs no system: with one distribution over micro states at both levels, EI(macro) = I(f(X); f(Y)) ≤ I(X; Y) = EI(micro) by data processing. Hoel’s causal emergence uses the uniform distribution at each level, which is a non-uniform micro distribution whenever blocks differ in size, so its positive values come from the micro chain scored under that other distribution. Comolatti and Hoel (LIT-1843) concede the stationary case; Eberhardt and Lee (LIT-1839) name the distribution as the source of the artefact. It says nothing about measures that data processing does not bound, nor about whether EI’s level agrees with an interventionist test. | Active |
| THEORY-1168 | In a Lotka–Volterra community with a symmetric interaction matrix, the growth-weighted biomass rᵀx strictly increases along every edge of the invasion graph, so the invasion graph has no cycles | Re-derived from Serván and Allesina (2021), LIT-1824, read in NOTE-1422, and applied to Hofbauer and Schreiber’s invasion graph (LIT-1233). At an equilibrium V = 2rᵀx − xᵀAx equals rᵀx, and for two equilibria the difference is a sum of invasion growth rates weighted by abundances, which an edge of the invasion graph makes positive. It needs symmetry and one equilibrium per vertex, not positive definiteness. It does not say assembly is order-independent: an indefinite symmetric matrix has several sinks. | Active |
| THEORY-1169 | For a discrete mechanism scored with one full-support intervention distribution over micro causes at both levels, a coarse-graining of cause and effect keeps all of the micro effective information if and only if it merges only causes with identical rows P(Y | do(x)) and only effects with proportional columns, whatever the distribution; so the coarsest coarse-graining that ties the micro is the causal partition of causal feature learning, with effects grouped by normalized likelihood, and any merge of causes with different effects loses information under every such distribution | Causal feature learning (LIT-1833, LIT-1834) defines macro causes as classes of micro states with the same interventional effect, with no distribution over interventions. Under one full-support distribution w at both levels, the loss of effective information from a coarse-graining (f, g) is I(X; Y | g(Y)) + I(X; g(Y) | f(X)), and both terms vanish exactly when f merges only equal rows and g only proportional columns, for every w. So the ties that THEORY-1167 allows are the causal-feature-learning partitions and their refinements: on which coarse-graining loses nothing, EI under a common distribution and the interventionist test agree, and the agreement is distribution-free. How much a merge loses still depends on w. Hoel’s EI, uniform at each level, parts from it on Eberhardt and Lee’s (13), (14) and note 6. | Active |
| THEORY-1170 | A convex map between two scenarios’ model sets is induced by a classical adaptive procedure exactly when some non-contextual model of the corresponding adaptive hom scenario induces it | The adaptive analogue of Theorem 44 that Barbosa, Karvonen and Mansfield assert in Closing Bell (LIT-845, §6.2) without proof, split from THEORY-174 when the fifteenth status review narrowed that entry to the non-adaptive procedures its re-derivation covers and promoted it (ADR-047, kind 1: a dropped clause the source asserts). The non-adaptive route does not transfer as it stands, since Lemma 39 fails for adaptive procedures. Proposed until a proof is read or re-derived. | Proposed |
| THEORY-1171 | In groups that build a new communication system, larger groups make it more systematic, and the greater variety of input they face drives the effect | The wide form of Raviv, Meyer and Lev-Ari (2019), LIT-825, kept here when the fifteenth status review narrowed THEORY-164 to what their experiment showed and promoted it (ADR-047, kind 1). The paper asserts that larger groups make an emerging language more systematic and that the greater variety of input they face drives the effect. One laboratory study with two group sizes found the size effect, and the mechanism rests on lagged association within its data; whether the effect replicates, and whether variability causes it, is open. | Proposed |
| THEORY-1172 | Linear mode connectivity emerges during training, not at initialization: copies trained from a shared state become stable to SGD noise after 1.5–20% of training, and independently trained networks become linearly connected after alignment only gradually | The wide form THEORY-114 held before the tenth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-114, Active, is its evidence. | Proposed |
| THEORY-1173 | Testimonial injustice is an ingenuous misjudgement of a speaker’s credibility caused by prejudice, not a deliberate manipulation of it, and it can be structural and pre-emptive, when a speaker’s word is never sought because of a structural prejudice that is no one’s fault | The wide form THEORY-327 held before the twelfth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-327, Active, is its evidence. Fricker states the account as what testimonial injustice is, not only as her usage; the record holds it as hers, in two papers read in full. Whether the book states it so, and whether it is right about the wrong, is open. | Proposed |
| THEORY-1174 | Industry can bias a scientific community toward a worse treatment without corrupting any individual, by selectively funding researchers whose methods already favour its product, provided researchers differ in method and both influence and the training of newcomers follow productivity; an independent funder that discounts industry-funded work counteracts this, and one that funds on productivity alone makes it worse | The wide form THEORY-146 held before the eleventh status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-146, Active, is its evidence. The old title’s “counteracts this only if it discounts” is restated as “that discounts … counteracts this”: the paper compares two funder policies and asserts no necessity, a mis-statement left with THEORY-146’s note. | Proposed |
| THEORY-1175 | Between tests, implementation intentions in the contingent if-then format had larger effects than plans that schedule when, where and what without linking cue to response (d = .43 against .29); rehearsing the plan once raised the effect, keeping a copy to revisit lowered it (.31 against .44), and adding how or for how long to a time-and-place cue roughly halved it | The wide form THEORY-908 held before the tenth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-908, Active, is its evidence. Sheeran, Listrom & Gollwitzer (2024), LIT-1488, conclude that the if-then format leads to superior impact, that rehearsal helps and that revisiting a kept copy makes plans less effective; their evidence is between-test moderator contrasts, uncorrected for bias. | Proposed |
| THEORY-1176 | Implementation intentions affect performance only when the goal intention they serve is strong and activated, so the cue-triggered response is gated by the goal and does not fire on the cue alone | The wide form THEORY-904 held before the tenth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-904, Active, is its evidence. The title is the old title’s general clause; its evidence clause read the 2024 moderator (d = .79) as a plan effect, a mis-statement left with THEORY-904’s note. | Proposed |
| THEORY-1177 | For experiments on a finite parameter set, being at least as informative for every decision problem is the same as being able to simulate the other by a randomisation | The wide form THEORY-156 held before the twelfth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-156, Active, is its evidence. Blackwell (1953), LIT-781, claims the equivalence for any outcome space, through Theorem 2, quoted from his 1951 paper. The record’s re-derivation reaches only outcome spaces that are standard Borel, since its last step needs a regular conditional distribution. | Proposed |
| THEORY-1178 | In slices of striatum, visual and prefrontal cortex and hippocampus, Hebbian co-activation leaves a synaptic eligibility trace, lasting about 1 s in striatum, 3 to 10 s in cortex and about 2 s in CA1, that a later neuromodulator or plateau potential converts into a weight change and whose sign it can set: experimental support for three-factor learning rules on behavioural time scales | The wide form THEORY-909 held before the tenth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-909, Active, is its evidence. Gerstner, Lehmann, Liakoni, Corneil & Brea (2018), LIT-1494, read five experimental papers as a decaying eligibility trace whose conversion, and direction, a third factor sets, and as support for three-factor rules on behavioural time scales; the evidence is mostly slices, one laboratory per region, and the reviewers grant that other mechanisms could bridge the gap. | Proposed |
| THEORY-1179 | In an active-inference model of post-traumatic context inference, an overly precise prior that one is in a harmful context makes exploratory sampling look uninformative, so the agent attenuates the periphery, never receives the evidence that would correct the prior, and the belief sustains itself; lowering precision removes the symptoms without correcting the prior | The wide form THEORY-285 held before the eighth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-285, Active, is its evidence. Linson et al. (2025), LIT-983, recast post-traumatic stress as lost context disambiguation and offer the loop as its mechanism; their simulations show it once per phenotype, with unreported parameters, and fit no patient data. | Proposed |
| THEORY-1180 | In foraging tasks, higher stress or anxiety goes consistently with less exploration, and in one task with a predator to check for, people higher in somatic anxiety checked less and did worse, a reduction associated with greater aversion to detecting the predator | The wide form THEORY-907 held before the thirteenth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-907, Active, is its evidence. | Proposed |
| THEORY-1181 | The content of a crowd-built r/place artwork is decided off the canvas, in negotiation through shared design images, where a few central members admit or refuse additions, and carried out by placers who mostly never join the discussion, so the placement record shows the outcome of coordination but not who directed it or who cooperated | The wide form THEORY-218 held before the tenth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-218, Active, is its evidence. Litherland & Mørch (2021), LIT-1037, give a framework in which the image on the canvas carries out a design decided in the forum, and argue that placement data cannot show cooperation, conflict or affiliation; they studied one artwork, and call the link from forum power to placements unclear. | Proposed |
| THEORY-1182 | Across seven computational learning studies selected without a systematic search, anxiety goes with altered adjustment of learning rate to uncertainty, mostly for aversive outcomes, while overall learning rate, choice consistency and outcome valuation show little relation to it | The wide form THEORY-897 held before the thirteenth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-897, Active, is its evidence. | Proposed |
| THEORY-1183 | Crowd-maintained r/place images persist as an equilibrium of attack and repair, and their abrupt overthrow is preceded by several distinct precursors, including the defenders’ own conduct, rather than by one generic warning signal, while many overthrows give no warning | The wide form THEORY-214 held before the twelfth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-214, Active, is its evidence. Falmagne, Stephenson and Levin (2026), LIT-1025, frame a defended image as an equilibrium of attack and repair and read several of the precursors of its overthrow as the defending community’s conduct. The framing is presupposed by their state variable, and the social reading is their own conjecture from SHAP curves. | Proposed |
| THEORY-1184 | In three laboratory studies of healthy humans, offering a costless avoidance response for a stimulus never paired with the aversive outcome led people to use it, and withdrawing the response then raised their expectancy of the outcome for that stimulus; signalling of the response is a confound | The wide form THEORY-920 held before the thirteenth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-920, Active, is its evidence. The old title’s clause “though not their skin conductance or startle in the one study that measured them” is not kept: it read more into the review than it says, and THEORY-920’s note of 2026-10-30 says why. | Proposed |
| THEORY-1185 | Merging models trained on different tasks from different initialisations fails where their features have no counterpart in the other model, and such features grow more common with depth | The wide form THEORY-113 held before the eleventh status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-113, Active, is its evidence. | Proposed |
| THEORY-1186 | Across computational studies of exploration in reward-based bandit tasks, mostly in sub-clinical samples and not yet replicated, directed exploration tends to rise with trait or cognitive anxiety and to fall with state or somatic anxiety | The wide form THEORY-917 held before the thirteenth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-917, Active, is its evidence. The old title’s last clause, that random exploration shows no relation to anxiety, is not kept: the review reports only that no study links them, and THEORY-917’s note of 2026-10-30 says why. | Proposed |
| THEORY-1187 | Along a low-loss linear path between two networks, every layer’s features are the interpolation of the endpoints’ features | The wide form THEORY-111 held before the eleventh status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-111, Active, is its evidence. The old title’s averaging clause was the record’s own step and is a Proposed claim of its own; the promote_when here is the layerwise half of the old one. | Proposed |
| THEORY-1188 | Once the architecture’s symmetries are factored out, most of the linear barrier between independently trained solutions disappears; the group that matters is the full one, permutations for MLPs and CNNs but for transformers also an orthogonal map on the residual stream, without which a barrier remains; and the barrier left after alignment falls with width | The wide form THEORY-112 held before the eleventh status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-112, Active, is its evidence. The old title’s last words, that the barrier left after alignment rises with depth, were the record’s composition, not a source’s, and are a Proposed claim of their own. | Proposed |
| THEORY-1189 | In laboratory avoidance learning in healthy humans, an avoidance response that remains available during extinction persists, in some participants for hundreds of unpunished trials, and keeps expectancy of the aversive outcome higher than in people denied it; the more effective and the cheaper the response, the slower it extinguishes | The wide form THEORY-901 held before the thirteenth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-901, Active, is its evidence. | Proposed |
| THEORY-1190 | In a Markov decision process, an agent that evaluates actions as if it will fail to avoid danger at later steps, while in fact choosing optimally at each step, spreads threat value to states far from the danger and avoids early and widely, which reproduces qualitatively exaggerated threat appraisal, fear generalization and several laboratory findings associated with anxiety | The wide form THEORY-915 held before the thirteenth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-915, Active, is its evidence. Zorowitz, Momennejad and Daw (2020), LIT-1496, state it of Markov decision processes in general and show it in the environments they simulate. The inherited promote_when asks for data in people, which the paper leaves to future work. | Proposed |
| THEORY-1191 | In a simulated active inference agent, a habit learned by counting the agent’s own state transitions and policy choices emerges from goal-directed behaviour, and once acquired it persists, and reinforces itself, after the reward is devalued, while an agent devalued before acquisition switches at once | The wide form THEORY-923 held before the tenth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-923, Active, is its evidence. | Proposed |
| THEORY-1192 v2 | Across 642 experimental tests to September 2019, forming implementation intentions reliably improved behaviour, cognitive performance, affect regulation and social judgement, but publication bias was substantial: the pooled d = .36 falls to a model-averaged d = .15 under robust Bayesian meta-analysis, with large heterogeneity | The wide form THEORY-918 held before the tenth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-918, Active, is its evidence. Sheeran, Listrom & Gollwitzer (2024), LIT-1488, find a robust overall effect after correction for publication bias and report benefits in all four outcome domains; only the overall estimate was corrected, and within behaviour vaccination and voting did not differ from zero. | Proposed |
| THEORY-1193 | How far fear falls during an extinction or exposure session, or across sessions, does not predict how much fear is expressed at follow-up, in animals, human laboratory samples and fearful human samples | The wide form THEORY-921 held before the fourteenth status review narrowed it, kept as a Proposed reading by the ADR-047 kind-1 sweep of 2026-10-30: the source asserts it, and THEORY-921, Active, is its evidence. | Proposed |
| THEORY-1194 | Clark and Chalmers argue that if belief is individuated by functional role, an external store that is constantly consulted, directly available and automatically endorsed can carry a standing belief, so that the material vehicles of some mental states extend beyond the skin; the step from coupling to parthood rests on that premise and on a parity principle they state rather than argue | What the extended-mind paper argues, split from THEORY-579 by the sixteenth status review on THEORY-1110’s pattern (ADR-058’s route), so that CLAIM-175, which argues “on the extended-mind thesis’s own terms”, can stand on the statement of those terms. Both papers were read in full (NOTE-180, NOTE-363), and Clark (2005) says in his own words that the parity principle was not argued. Whether the conditional holds, that coupling of this kind makes a store part of a mind, stays THEORY-579’s question, Proposed. | Active |
| THEORY-1195 | About 800 Myr ago the breakup of the Eulalia parent body beside the Jupiter 3:1 resonance sent an impact shower to the terrestrial planets and the Moon that made the cluster of large lunar craters dated near 800 Ma | The thesis of Bottke et al. (2026), LIT-009, in its title, kept here when the twenty-second status review narrowed and promoted THEORY-499, the reading of the plausibility model (ADR-065; ADR-047 kind 1). The model shows that a source could have done it; only Copernicus of the seven craters has a sample age. | Proposed |
| THEORY-1196 | During a visual decision task, neurons within a single area of mouse cortex rarely form discrete functional types, yet the task conditions the area distinguishes are linearly separable in nearly every way | The wide form of Posani et al. (2026), LIT-708, kept here when the status review of 2026-10-30 narrowed THEORY-124 to what their analysis of the IBL Brainwide Map measured and promoted it (ADR-065; ADR-047, kind 1). The paper asserts that cortical representations are rarely categorical and highly separable. One task, overtrained mice, eight variables and a lenient separability criterion. | Proposed |
| THEORY-1197 | Eukaryogenesis involved one archaeal host lineage, of Asgard descent, and one bacterial endosymbiont, the alphaproteobacterial ancestor of mitochondria; the eukaryotic genes from other bacteria came by piecemeal gene transfer, not from further symbiotic partners | The wider thesis Tobiasson, Luo, Wolf & Koonin assert, filed beside THEORY-1104 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1104, Active, holds what Tobiasson and colleagues’ survey finds and how the authors read it; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1104’s old condition, word for word. | Proposed |
| THEORY-1198 | Unlawful states of emergency, in declaration, conduct or duration, follow political turmoil far more often than natural disasters, are rarer in democracies than in autocracies, and last much longer than lawful ones | The thesis of Bjørnskov, Voigt & Khesali’s abstract (2022; working paper 2021), LIT-1473, kept here when the twenty-second status review narrowed THEORY-911 to the counts the paper reports and promoted it (ADR-065; ADR-047 kind 1). Its coding of lawfulness is from news and NGO reports, and part of the duration gap is built in by the coding. | Proposed |
| THEORY-1199 | Real-world games of skill have a spinning-top geometry: their non-transitive part, measured as Nash cluster size, is largest at intermediate strength and narrows toward the strongest and the weakest strategies | Czarnecki et al.’s hypothesis (LIT-1504, read in NOTE-1146), filed beside THEORY-930 when the status review of 2026-10-30 narrowed and promoted that entry under ADR-065 (ADR-047 kind 1). The paper’s body says it does not prove that real games have this geometry; its evidence is THEORY-930’s sampled profiles, whose shape the sampler and the maximum-entropy equilibrium help set. | Proposed |
| THEORY-1200 | The Asgard archaeal ancestor of eukaryotes depended on metabolic partners: like Candidatus Prometheoarchaeum syntrophicum, it degraded amino acids in syntrophy, handing hydrogen and formate to partners that removed them | The wider thesis Imachi et al. assert, filed beside THEORY-1108 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1108, Active, holds what Imachi and colleagues’ cultivation shows and what they infer from it; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1108’s old condition, word for word. | Proposed |
| THEORY-1201 | Normalized stem length is not a clock of gene acquisition time: it is set mainly by factors other than when a gene was acquired, such as adaptation to the new cell after acquisition, so relative timings of eukaryogenesis drawn from stem lengths alone are not supported | The wider thesis Tobiasson, Luo, Wolf & Koonin assert, filed beside THEORY-1101 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1101, Active, holds what Tobiasson and colleagues find and conclude; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1101’s old condition, word for word. | Proposed |
| THEORY-1202 | A securitised public keeps its routines by not attending to routine security practices, which keeps an anxiety about the threat latent rather than absent; when the security apparatus itself disrupts those routines the anxiety surfaces, and with it blame of the apparatus | Ku and Finch’s ontological agency (LIT-1478, read in NOTE-1133), filed beside THEORY-898 when the status review of 2026-10-30 narrowed and promoted that entry under ADR-065 (ADR-047 kind 1). The Gangneung observations illustrate it; inner states were not measured, and habituation and low perceived risk were not tested against it. | Proposed |
| THEORY-1203 | The host lineage elaborated its cytoskeleton, endomembrane system and nuclear machinery before mitochondrial endosymbiosis began, about 2.2 billion years ago: most pre-LECA duplications in eukaryotic gene families of archaeal origin predate it | The wider thesis Kay et al. assert, filed beside THEORY-1099 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1099, Active, holds what Kay and colleagues’ dating finds and how the authors read it; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1099’s old condition, word for word. | Proposed |
| THEORY-1204 | The strongest evidence that a quality-space model targets phenomenal experience, and not only behaviour or neural activity, is convergence between models of the same space derived through different behavioural procedures, since experience is what those procedures share | Isaac’s “own considered view” (2025), LIT-1361, §5, kept here when the twenty-second status review narrowed THEORY-953 and promoted it as a report (ADR-065; ADR-047, kind 1). The argument does not rule out a shared stimulus geometry or a shared response process as the common factor, and the convergence is partial by the paper’s own account. | Proposed |
| THEORY-1205 | Eukaryotes began in a syntrophic partnership: an archaeal host fermented sugars and passed reducing equivalents to an alphaproteobacterial endosymbiont that contributed a TCA cycle and an electron transport chain, which is why the last eukaryotic common ancestor’s central carbon metabolism is archaeal in cytosolic glycolysis and the pentose phosphate pathway and alphaproteobacterial in the mitochondrial TCA cycle | The wider thesis Santana-Molina, Williams, Snel & Spang assert, filed beside THEORY-1109 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1109, Active, holds what Santana-Molina and colleagues find and how they read it; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1109’s old condition, word for word. | Proposed |
| THEORY-1206 | The mitochondrion was acquired late in eukaryogenesis, by a host whose proteome was already chimaeric, with genes from several bacterial sources acquired before it | The wider thesis Pittis & Gabaldón assert, filed beside THEORY-1102 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1102, Active, holds what Pittis and Gabaldón’s analysis finds and how the authors read it; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1102’s old condition, word for word. | Proposed |
| THEORY-1207 | Russian military writers of 2015–2020 use ‘hybrid war’ for a category of war marked off by its objective, reshaping a target state’s governance, geostrategic orientation and worldview, in which every action up to conventional military force is subordinate to an information campaign, and not, as in Western usage, for a set of means below the threshold of armed conflict | The wide form of Clark (2020), LIT-023, kept here when the status review of 2026-10-30 narrowed THEORY-488 to what Clark’s synthesis reports and promoted it (ADR-065; ADR-047, kind 1). Clark asserts that the definition is the Russian military’s own and institutional. His sources were chosen by no stated rule, a handful of authors carry much of the weight, and the report predates the 2022 invasion. | Proposed |
| THEORY-1208 | Bacterial endosymbionts lose their cell-envelope and envelope-transport genes together below about 400 kb and begin to lose translation genes below about 200 kb, and the host supplies the membranes, transport and protein synthesis that the smallest-genome symbionts no longer encode, as for organelles | The wider thesis McCutcheon, Garber, Spencer & Warren assert, filed beside THEORY-1049 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1049, Active, holds what McCutcheon and colleagues’ survey shows and what they infer from it; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1049’s old condition, word for word. | Proposed |
| THEORY-1209 | In genetically identical E. coli, a cell’s swarming potential is a transient inherited state: its descendants share it for about four generations and lose it by about seven, and it tracks the cell’s iron status rather than a bistable switch | The wide form of Bhattacharyya et al. (2023), LIT-853, kept here when the status review of 2026-10-30 narrowed THEORY-179 to what the assays measured and promoted it (ADR-065; ADR-047, kind 1). The paper asserts a heritable iron memory. Iron was read only through a plasmid promoter reporter, inheritance rests on few founders and four sampled generations, and the delay model is fitted to two time points. | Proposed |
| THEORY-1210 | When several networks are aligned, fitting one joint multi-marginal coupling finds held-out correspondences better than fitting them in pairs, and the gain comes from the joint fit itself, not from the cost or the search space that come with it | Zeng et al.’s (2024) attribution of HOT’s gains to joint alignment (NOTE-1334’s C6, asserted without an ablation), kept here when the twenty-second status review narrowed and promoted THEORY-1159 (ADR-065; ADR-047 kind 1). No ablation in the record holds the RWR cost and the clustering fixed, and every benchmark’s truth is consistent by construction. | Proposed |
| THEORY-1211 | An endosymbiont becomes an organelle in steps: the host first targets effector proteins into it; an imported host protein redundant with one of its functions then lets the endosymbiont’s own gene decay, making it dependent; and a general import pathway, once evolved, brings in hundreds of proteins; this genetic integration arises only in permanent, vertically transmitted associations | The wider thesis Sørensen, Stiller, Kröninger & Nowack assert, filed beside THEORY-1107 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1107, Active, holds the scenario Sørensen and colleagues propose; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1107’s old condition, word for word. | Proposed |
| THEORY-1212 | In 30 four-person student groups discussing 15 choice dilemmas, a member’s self-reported closure to influence on the next issue rose with their influence over prior outcomes, increasingly so along the sequence, and the groups’ influence networks thinned and their discussions shortened while the rate of consensus did not change: evidence for a reflected-appraisal step by which influence concentrates in deliberating groups | The wide form of Friedkin, Jia and Bullo (2016), LIT-1482, kept here when the status review of 2026-10-30 narrowed THEORY-902 to what their experiment measured and promoted it (ADR-065; ADR-047, kind 1). The authors argue that a reflected-appraisal step, closure set by realized influence, concentrates influence in deliberating groups. Closure and influence came from one self-report, prior closure was not controlled, and the predicted end state was not reached. | Proposed |
| THEORY-1213 | In relational quantum mechanics as Di Biagio and Rovelli reformulate it, classical subsystems whose variables couple properly, so as to get correlated, come to agree, so that the merging of perspectives answers the combination problem and the facts held relative to different outside systems never conflict about the same variables | The general claim of Di Biagio and Rovelli (2025), LIT-1676, p. 5: “If the variables couple correctly so as to get correlated, their perspectives will agree”. Kept here when the twenty-second status review promoted THEORY-1074 as a report of the worked examples (ADR-065; ADR-047, kind 1). Asserted, not proved. THEORY-621 and THEORY-1080 leave the same gap open. | Proposed |
| THEORY-1214 | Cicada hosts whose endosymbiont Hodgkinia has split into many interdependent lineages compensate by sending more Hodgkinia cells to each egg, with Sulcia numbers and the transmission route unchanged, so that every egg still receives every lineage; the raised titre is a host adaptation driven by the symbiont’s fragmentation, and a cost of it | The wider thesis Campbell et al. assert, filed beside THEORY-1106 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1106, Active, holds what Campbell and colleagues measured and how they read it; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1106’s old condition, word for word. | Proposed |
| THEORY-1215 | Besides Asgard archaea and the alphaproteobacterial ancestor of mitochondria, Myxococcota and Planctomycetota were major donors of genes to the eukaryotic lineage before its last common ancestor, in waves: Asgard first, then Planctomycetota before the mitochondrion, then the mitochondrial ancestor and Myxococcota together | The wider thesis Bernabeu, Manzano-Morales, Marcet-Houben & Gabaldón assert, filed beside THEORY-1105 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1105, Active, holds what Bernabeu and colleagues’ reconstruction finds and how the authors read it; whether that is true is this entry’s question, and its promote_when is THEORY-1105’s old condition, word for word. | Proposed |
| THEORY-1216 | Ill structured problems can be handled by an alternation between a solver working on a problem that is well structured at each moment and a recognition and retrieval system that keeps modifying the problem space from memory or the environment, a serial solver gains nothing by assembling the problem space at the outset, and nothing but the size of the knowledge base may separate ill from well structured problems, so that no qualitatively new mechanisms are needed | The thesis Simon (1973), LIT-1634, proposes, kept here when the twenty-second status review promoted THEORY-1084 as a report of the proposal (ADR-065; ADR-047, kind 1). The paper describes the architecture, matches it to an architect, to battleship design and to a chess program, and argues from the seriality of the solver; nothing is built or tested, and Simon states the last part as what his analysis “suggests”. | Proposed |
| THEORY-1217 | Both owner ideology and favor exchange drove the Hungarian portal Origo’s reduced coverage of corruption in 2013–2016: favor exchange alone cut it by 29–44%, the new owner’s ideology alone by 63% after 2016, and the two together by 74%, so they are substitutes; and a ban on targeted government advertising would have raised it by 41–79% | The finding of Szeidl and Szucs (2021), LIT-1315, without the condition on their identifying assumptions, which the authors call “arguably strong” for print and weaker for online. Kept here when the twenty-second status review promoted THEORY-852 as the conditional estimate (ADR-065 §3 and §7; ADR-047, kind 1). | Proposed |
| THEORY-1218 | In a sparsely-gated mixture-of-experts layer trained without balancing losses, the gate’s concentration on a few experts arises by self-reinforcement: favoured experts are trained more rapidly and so are selected still more | The authors’ explanation in Shazeer et al. (2017), LIT-1507, p. 5, stated and not tested. Kept here when the twenty-second status review promoted THEORY-927 as the report (ADR-065; ADR-047, kind 1). | Proposed |
| THEORY-1219 | Buchnera’s metabolism interlocks with its aphid host’s: it makes the essential amino acids its host cannot from host-supplied glutamate and aspartate, depends on the host for the non-essential amino acids and its membrane phospholipids, and cannot live outside the bacteriocyte | The wider thesis Shigenobu, Watanabe, Hattori, Sakaki & Ishikawa assert, filed beside THEORY-1103 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1103, Active, holds what Shigenobu and colleagues’ genome shows and what they infer from it; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1103’s old condition, word for word. | Proposed |
| THEORY-1220 | A graph network that learns its sheaf restriction maps from node features succeeds on heterophilic graphs because it learns the class-aligned transports its separation theory prescribes: sign flips or rotations across classes, identity within them | The wider thesis of Bodnar et al. (2022), LIT-1811, kept here when the twenty-second status review promoted THEORY-1139, the reading of what was measured (ADR-065; ADR-047 kind 1). The learned maps were inspected only in the synthetic bipartite case; whether the maps learned on real graphs have this geometry, and whether accuracy depends on it, is open. | Proposed |
| THEORY-1221 | Anger makes fake news viral online: on Weibo fake news carries more anger and less joy than true news, and the anger in a post causes it to be shared more | Chuai and Zhao’s (2020) thesis, LIT-379, kept here when the twenty-second status review narrowed THEORY-329 to the association their corpus measured and promoted it (ADR-065; ADR-047 kind 1). The design is observational, and the fake set is selected for having spread. | Proposed |
| THEORY-1222 | In relational quantum mechanics as stated in Rovelli (1996), rules (i) and (ii), that there is no state except within a further observer’s information and no information without interaction, exclude any contradiction between observers’ views: what a third system predicts of two observers’ information always agrees with what it finds on interacting with them | Rovelli’s general consistency claim (1996), LIT-1635, §III.D, p. 15, kept here when the twenty-second status review promoted THEORY-1080 as a report (ADR-065; ADR-047, kind 1). Shown for one measurement (p. 9) and introduced in general with “The reader may convince himself”. | Proposed |
| THEORY-1223 | Monocercomonoides exilis lost its mitochondrion only after the organelle’s essential functions had been removed in steps, Fe–S cluster assembly to a cytosolic SUF system and then the glycine cleavage system by loss, and the loss required no compensating change elsewhere in the cell | The wider thesis Karnkowska et al. assert, filed beside THEORY-1098 by the twenty-second status review (ADR-065 §3; ADR-047 kind 1). THEORY-1098, Active, holds what Karnkowska and colleagues’ genome analysis finds and infers; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1098’s old condition, word for word. | Proposed |
| THEORY-1224 | In Claude language models, projecting out the most active J-space directions in early workspace layers lowers the rate of felt, first-person, sensory language in the models’ narrations of their own processing and in their descriptions of another person’s experience, while norm-matched perturbations along other directions do not and the text stays coherent; so in these models the experiential register of report depends on the access-like workspace and is not specific to self-report | The wide form of Gurnee, Sofroniew et al. (2026), LIT-1347, section 3.5.3, kept here when the status review of 2026-10-30 narrowed THEORY-869 to what the ablation measured and promoted it (ADR-065; ADR-047, kind 1). The authors conclude that “the J-space supports the model’s propensity to provide rich experiential reports, whether about itself or another entity” (p. 28). The measure is a model-graded register on few prompts, in one company’s models, with no register control and no blind human rating. | Proposed |
| THEORY-1225 | Among white Southerners today, those living in counties where a larger share of the 1860 population was enslaved are somewhat less Democratic, less supportive of affirmative action and more racially resentful, by about a tenth of a standard deviation per standard deviation of slave share, and colder toward black Americans, by about a third; the difference is not accounted for by the present black share of the population, and in voting it appeared after Reconstruction rather than before the war, which supports its origin in the incentives that emancipation gave planters to repress black labor and votes, and its local transmission thereafter | The wide form of Acharya, Blackwell and Sen (2016), LIT-1388, kept here when the status review of 2026-10-30 narrowed THEORY-889 to what the analysis measured and promoted it (ADR-065; ADR-047, kind 1). The paper argues that the attitude difference originated in emancipation’s incentives to repress black labor and votes and was transmitted locally. The causal reading rests on an untestable exclusion restriction, residence stands in for descent, and the transmission evidence is not tied to county slavery. | Proposed |
| THEORY-1226 | In Claude language models, a sparse set of residual-stream directions that a corpus-averaged Jacobian lens identifies as verbalizable (the J-space) is causally privileged for verbal report, for holding instructed concepts, for unspoken intermediate steps of reasoning and for passing one argument to many functions, while continuation, anomaly detection and line wrapping use the same information without routing through it; it carries workspace-like content only in a middle band of layers, holds on the order of tens of active directions and under a tenth of activation variance, and is amplified and relayed by the weights more than other directions | The wide form of Gurnee, Sofroniew et al. (2026), LIT-1347, kept here when the status review of 2026-10-30 narrowed THEORY-865 to what their experiments measured and promoted it (ADR-065; ADR-047, kind 1). The paper asserts that verbalizable representations form a global workspace in language models. Its tests are on four models of one family, by their makers, with a selectivity split partly defined by the result; no independent replication is reported. | Proposed |
| THEORY-1227 | Haken, Kelso and Bunz model the switch of rhythmic bimanual coordination from anti-phase to in-phase at a critical frequency as the loss of one stable state of an order parameter, relative phase, derived from two coupled oscillators; Kelso, Scholz and Schöner report the variability of relative phase rising before the switch in the anti-phase pattern only, in a few subjects and with no statistical test | What the Haken–Kelso–Bunz paper proposes and what the first report of critical fluctuations measured, split from THEORY-069 by the twenty-third status review on THEORY-1110’s pattern (ADR-058, ADR-065), so that a claim needing only the model and that report can stand on it. Both papers are read in full (NOTE-1424, NOTE-1433). Whether the switch is a nonequilibrium phase transition with critical slowing and hysteresis as its warning signs, which needs relaxation-time and hysteresis data neither paper shows, stays THEORY-069’s question, Proposed. | Active |
| THEORY-1228 | A bacterial endosymbiont becomes genetically integrated, an organelle, when host proteins imported into it replace genes it has lost, and this does not require gene transfer from the endosymbiont: in the Paulinella chromatophore and the nitroplast, the two systems with hundreds of imported proteins, the replacing genes are mostly the host’s own or come from other bacteria | The wider thesis Sørensen, Stiller, Kröninger & Nowack assert (“EGT is not a precondition for the genetic integration of an endosymbiont”), filed beside THEORY-1100 by the twenty-third status review (ADR-065 §3; ADR-047 kind 1). THEORY-1100, Active, holds what the review reports; whether the thesis holds is this entry’s question, and its promote_when is THEORY-1100’s old condition, word for word. | Proposed |
| THEORY-1229 | Formal emergency powers, extraordinary powers functionally equivalent to them and emergency rhetoric are linked to the accelerated erosion or dismantling of democracy and to the consolidation of autocratic rule, though the convergence is not inevitable | The wider thesis Dagan and Benvenisty assert (“the study demonstrates a clear link”, para. 12), filed beside THEORY-906 by the twenty-third status review (ADR-065 §3; ADR-047 kind 1). THEORY-906, Active, holds what their summary reports of five cases chosen because they autocratized; whether the link holds is this entry’s question, and its promote_when is THEORY-906’s old condition, word for word. | Proposed |
| THEORY-1230 | In relational quantum mechanics, with facts fixed by interaction and the classical sum rule used only within one context or where facts are stable, facts relative to different systems never yield contradictory predictions in extended Wigner’s-friend scenarios, and a superobserver’s later facts agree with his friend’s | The consistency Di Biagio and Rovelli claim for relational quantum mechanics, filed beside THEORY-1081 by the twenty-fourth status review (ADR-065 §3; ADR-047 kind 1). THEORY-1081, Active, holds what they argue; whether relative facts cohere in general is this entry’s question, with THEORY-1081’s old condition. | Proposed |
| THEORY-1231 | When each agent’s Q-function is approximated as an average of pairwise terms and expanded about the mean action of its neighbours, the first-order term vanishes and the approximation error is a second-order remainder bounded by the curvature of the pairwise Q-function, leaving a two-body problem between an agent and its neighbours’ average; with homogeneous agents, mean field Q-learning converges to the Nash Q-value under assumptions the authors call strong, and learned tasks of 500 and 1000 agents where independent and centralized-critic baselines failed | The wide form of Yang et al. (2018), LIT-1512, kept here when the twenty-fourth status review narrowed THEORY-945 to the re-derived expansion and to what the paper states and ran, and promoted it (ADR-047, kind 1). The paper asserts that mean field Q-learning converges to the Nash Q-value under its assumptions, and that it makes many-agent learning tractable. Its proof does not reconcile a high-temperature contraction with a greedy limit, and its many-agent evidence is one task at two sizes. | Proposed |
| THEORY-1232 | Under reflected appraisal across issues, whether power concentrates in one member depends on the single-issue step: with Friedkin–Johnsen anchoring on initial positions almost every random strongly connected group evolves to a single leader, and with DeGroot consensus the same random complete networks keep power spread | The general contrast, filed beside THEORY-1161 by the twenty-fourth status review (ADR-065 §3; ADR-047 kind 1). THEORY-1161, Active, holds what Friedkin’s simulations showed; whether the anchored step’s autocratic fixed points attract almost every start, and the DeGroot step’s do not, is this entry’s question. Re-runs on sparse networks of density 0.4 gave 93% and 96% single leaders; the DeGroot side rests on THEORY-916, Proposed. | Proposed |
| THEORY-1233 | For the replicator flow of a finite game, every asymptotically stable sink chain component contains at least one sink strongly connected component of the weakly-better-response graph, a Markov-Conley chain | The half of Omidshafiei et al.’s Theorem 2.4.24 that THEORY-942 does not assert, kept here when the twenty-fourth status review promoted THEORY-942 on the other half (ADR-047, kind 1). The paper’s proof conjugates the interior flow to a volume-preserving one, and then argues inductively that an attractor reaches a vertex. NOTE-1156 found that step asserted, not carried out. | Proposed |
| THEORY-1234 | The replicator-plus-entropy model of Boltzmann Q-learning in two-player stateless games is exact for frequency-adjusted Q-learning, not for Q-learning, whose expected update carries an extra factor of each action’s selection probability and whose trajectories in 2×2 games depart from the model depending on initialization | The wide form of Kaisers & Tuyls (AAMAS 2010), LIT-1511, kept here when the twenty-fourth status review narrowed THEORY-932 to what the derivation proves and what their three games showed, and promoted it (ADR-047, kind 1). The paper asserts that the model is exact for frequency-adjusted Q-learning and that Q-learning departs from it depending on initialization. Its plots are three games, one temperature, compared by eye. | Proposed |
| THEORY-1235 | Losing a costly function whose product leaks to neighbours is favoured by ordinary individual selection in large free-living microbial populations, and the loss proceeds until the remaining producers just supply the community, so that most cells come to depend on a rare few with no relatedness, cooperation or collective required | The Black Queen Hypothesis itself, filed beside THEORY-1048 by the twenty-fourth status review (ADR-065 §3; ADR-047 kind 1). THEORY-1048, Active, holds what the hypothesis says; whether it is true is this entry’s question, with THEORY-1048’s old condition word for word. | Proposed |
| THEORY-1236 | Agency is relative to an observer: an identified system is an agent, for that observer, to the degree that a description of the function it optimises explains its behaviour better under the observer’s prior than any description of its input-output mapping | The relative definition of agency Orseau, McGill and Legg propose, filed beside THEORY-624 by the twenty-fourth status review (ADR-065 §3; ADR-047 kind 1). THEORY-624, Active, holds what the paper does and argues; whether the comparison is a criterion of agency for real systems is this entry’s question, with THEORY-624’s old condition word for word. | Proposed |
| THEORY-1237 | Instructed reappraisal lowers reported negative affect to aversive pictures while the responses of the amygdala, periaqueductal gray, hypothalamus and other subcortical regions to the same pictures show evidence of no change; the regions it reduces are cortical, mainly higher visual and parietal | The wider thesis Bo et al. assert (“subcortical affective processes are less modifiable by reappraisal than previously thought”, p. 20), filed beside THEORY-871 by the twenty-fourth status review (ADR-065 §3; ADR-047 kind 1). THEORY-871, Active, holds what their two midlife samples measured under one instructed strategy. Whether the result holds for reappraisal at large is this entry’s question, and its promote_when is THEORY-871’s old condition, without the version-of-record clause. | Proposed |
| THEORY-1238 | Disinformation incidents carried in STIX 2.1 as the DISINFOX mapping carries them are an interoperable representation that survives exchange between organisations, and sharing them in this form improves analysts’ correlation and exposure of incidents and their reuse of labels | The thesis Sánchez González et al. motivate, filed beside THEORY-651 by the twenty-fourth status review (ADR-065 §3; ADR-047 kind 1). THEORY-651, Active, holds the mapping and its demonstration; nothing beyond ingestion was measured, so whether the representation is faithful and whether sharing helps is this entry’s question, with THEORY-651’s old condition. | Proposed |
| THEORY-1239 | No logistic system, one that separates propositions from general laws of inference, can carry commonsense knowledge, whose defaults later evidence displaces: attempts to repair its monotonicity will continue to fail | Minsky’s (1974) further claim against logic, from the frames memo’s appendix (LIT-410, read in NOTE-337, C7). It was kept here when the twenty-fourth status review promoted THEORY-462 (ADR-065 §3; ADR-047, kind 1). Monotonicity is a correct observation about classical logic. The memo asserts that no repair can succeed: “I think such attempts will continue to fail”. The record holds no reading of the non-monotonic logics that were built to repair it. The condition is carried over word for word, so “the account” in it now means this entry, and “its first half” means THEORY-462. | Proposed |
| THEORY-1240 | Trained, instruction-tuned and preference-tuned chat models keep the nature of the idealized fiction machine: what they assert follows the narrative coherence of the frame, role or story the conversation sets up, not a representation of truth that stays fixed across frames | The wider thesis Bottou and Schölkopf assume, filed beside THEORY-547 by the twenty-fourth status review (ADR-065 §3; ADR-047 kind 1). THEORY-547, Active, holds what follows from their idealization; whether deployed chat models share that nature is this entry’s question, and its promote_when is THEORY-547’s old condition, word for word. | Proposed |
| THEORY-1241 | Experienced Transcendental Meditation practitioners report more pure awareness than matched counting controls, and multivariate EEG separates the meditation period from counting and from rest, but the reports are not shown to track any EEG feature | The general form of Chandia-Jorquera et al.’s finding, filed beside THEORY-870 by the twenty-fourth status review (ADR-065 §3; ADR-047 kind 1). THEORY-870, Active, holds what the one study measured; whether practitioners in general report more pure awareness, robustly to demand, and whether EEG separates the practice from other effortless ones, is this entry’s question. | Proposed |
| THEORY-1242 | In early-vision tasks, human performance varies across conditions as the information available at the retinal output does, while falling well below the retinal-stage ideal, so substantial losses lie in central factors | The thesis Geisler’s review asserts, filed beside THEORY-336 by the status review of 2026-10-30 (ADR-065 §3; ADR-047 kind 1). THEORY-336, Active, holds what the review reports; whether the parallel holds is this entry’s question, and none of the primary stage-by-stage studies (Geisler 1989; Banks, Geisler and Bennett 1987) is read. | Proposed |
| THEORY-1243 | In incipient endosymbioses in nature, mutual dependence evolves ahead of reproductive cohesion, so that endosymbioses are more likely to be mutually dependent than cohesive | The inference Athreya, Czuppon and Gokhale draw for nature, filed beside THEORY-1050 by the twenty-fourth status review (ADR-065 §3; ADR-047 kind 1). THEORY-1050, Active, holds the model result and its dependence on the trait mapping; whether real symbioses are dependence-first is this entry’s question, with THEORY-1050’s old condition. | Proposed |
| THEORY-1244 | No access method is optimal on read, update and memory overhead at once: bounding any two of the three forces the third above a hard lower bound that cannot be further reduced | The RUM conjecture as its authors intend it, filed beside THEORY-344 by the status review of 2026-10-30 (ADR-065 §3; ADR-047 kind 1). THEORY-344, Active, reports the conjecture and what its formal wording and toy extremes do and do not show; whether the trade holds, quantified, is this entry’s question. | Proposed |
| THEORY-1245 | Evaluating expected free energy recursively over the beliefs an agent would hold after each plausible outcome makes active inference a pruned tree search over belief states, formally analogous to Bellman recursion, which lets the agent plan through short-term costs that one-step agents cannot; that the pruning keeps deep search tractable beyond toy problems is argued, not shown | The general form of Friston, Da Costa, Hafner, Hesp and Parr (2020), LIT-577, under THEORY-426’s old title. It was kept here when the twenty-fourth status review narrowed THEORY-426 to the paper’s runs and promoted it (ADR-065 §3; ADR-047, kind 1). The paper shows the planning claim only in single deterministic runs on a T-maze and an 8 × 8 maze (NOTE-454, C2). It argues tractability from pruning and sparsity and counts evaluations for one maze (C3). It tries no problem where many outcomes stay plausible, and runs no Bayes-adaptive planner beside it. | Proposed |
| THEORY-1246 | The so-called contentless goal-states of Shamatha, Transcendental and Stillness Meditation are neither truly contentless nor identical: they lack thoughts, perceptions, images and memories but keep wakefulness, calm, stillness, a non-conceptual knowing and the like, and they differ across the practices in attentional stability | Woods, Windt and Carter’s thesis about the experiences, filed beside THEORY-866 by the twenty-fourth status review (ADR-065 §3; ADR-047 kind 1). THEORY-866, Active, holds what the teachers’ texts describe; whether practitioners’ experience is so is this entry’s question, with THEORY-866’s old condition. | Proposed |
| THEORY-1247 | Griesemer and Shavit propose, as a first and rough sketch, that a collective becomes a new level of individuality only when collaboration toward a shared goal, rather than coordination or cooperation, organizes it, some core interactions have become generatively entrenched, and it has organizational closure, and that such a community can be reproduced only by exporting an organized sample of its roles and interactions, not of its members alone | What Griesemer and Shavit’s sketch proposes. The twenty-fourth status review split it from THEORY-418 (ADR-065 §3), so that the record holds the reading of the proposal apart from the proposal. The paper was read in full (NOTE-173), so the reading is held. Whether the proposal is right is THEORY-418, Proposed, which extends this entry. That needs criteria that sort real groups into the three grades, and worked cases. The paper’s two headline claims, non-circularity and individuality as a special case of collectivity, are in its abstract only and are not part of this entry. | Active |
| THEORY-1248 | Catalysts cancel out of the stoichiometric matrix, so a cycle of mutual catalytic production among species is not a stoichiometric cycle: the cycles that carry a reaction network’s steady currents and affinities are fuel-to-waste pathways through it, and who catalyses whom enters only the rates, never the thermodynamic driving | From the definitions of Dal Cengio, Lecomte and Polettini (2023), LIT-1897 (NOTE-1476), and Rao and Esposito (2016), LIT-1889 (NOTE-1464), neither of which says it in these words. It makes exact A13’s “a productive cycle need not be a stoichiometric cycle” from the exchange “Analyze nucleation concepts”. Checked on a reversible rewriting of CASE-189’s first construction. Active: definitional and checked. It does not say that catalytic cycles are thermodynamically idle. They decide which of the states the driving allows is reached, and bistability needs them; but the budget they work within is set elsewhere. | Active |
| THEORY-1249 | In a fully observed, finite, communicating, stationary controlled Markov process, a deterministic goal-conditioned policy that achieves every composite goal of depth up to n with probability at least 1 − δ times the optimum determines every transition probability to within √(2P(1−P)/((n−1)(1−δ))), read from its first action on either-or goals; for a policy competent only at one-step goals no bound follows | Richens, Abel, Bellot and Everitt (2025), LIT-1891, Theorems 1 and 2, read in NOTE-1469. The reduction offers the agent a choice between “at most k successes of a transition in n attempts” and “more than k”; its switch point locates the binomial median. The final bound was re-derived and checked numerically against an adversarial δ-bounded agent. Active: a theorem, checked. It says the transition function is recoverable from the input-output map, not that any component of the agent represents it, and it needs full observation, determinism and the regret bound on every listed goal. | Active |
| THEORY-1250 | A chemostat is an emergent structure of a closed reaction network: when exchange reactions are fast and the reservoir species are abundant by a factor of order Omega, the closed network behaves to leading order as the open one, with its local detailed balance and dissipation, over a window that opens once exchange equilibrates and closes on a time of order Omega, after which a driven network relaxes to equilibrium; neither separation alone suffices | Remlein, Esposito and Avanzini (2026), LIT-1887, read in NOTE-1468: a multiscale expansion in the rate ratio ε and a WKB argument in the abundance ratio Ω, for arbitrary stoichiometry. The lifetime scaling was checked by integrating the paper’s §IX network, T_δ = 0.00483 Ω against its fit 0.0048 Ω + 0.33. Active. It does not say that every driven closed network departs from open behaviour at T ~ Ω, only that it can from then on, nor anything about systems that are not chemical. | Active |
| THEORY-1251 | Mossio, Montévil and Longo take organization, as closure of constraints, to be a theoretical principle of biology, posited a priori as physics posits its phase space and defining the domain together with variation, so that every system meeting both is biological by definition and organisms are one class of such systems; on this reading “organisms are organized” is constitutive, not an empirical finding, and the principle is to be judged by what it makes intelligible | Mossio, Montévil and Longo (2016), LIT-1888, §§1 and 4, read in NOTE-1461; the definitions are Montévil and Mossio’s (LIT-582, TERM-070). The paper states the principle’s status and scope and supports it by history and analogy; it derives nothing from it here. Proposed: what the principle buys is untested in this paper. It does not say that closure is observed in every organism, nor that only organisms realize it. | Proposed |
| THEORY-1252 | In ℓ2-regularized regression held to a fixed training-error tolerance, refitting to one’s own predictions on the same inputs shrinks each eigencomponent of the labels by a factor that falls with its Gram eigenvalue, while the regularization weight needed to meet the tolerance rises as the labels shrink, so repeated rounds amplify regularization and reach the zero function after finitely many; the loss comes from the regularizer acting again, not from information the student lacks | Mobahi, Farajtabar and Bartlett (2020), LIT-1895, eqs. 24–37 and §§3.2–4; read in NOTE-1478, with the paper’s illustrative example reproduced from its own sample values. Active for the recurrence, the rising multiplier and collapse, which are elementary and reproduced; the sparsity rate of Theorem 5 is the paper’s, proof not checked. It does not show that deep networks behave so, and the amplification depends on holding the error tolerance fixed. | Active |
| THEORY-1253 | Treating the Bayesian evidence as a partition function with sample size as inverse temperature, the analogue of heat capacity, the rate at which leave-one-out predictive loss falls with sample size, equals half the parameter count in a regular model, as equipartition, and the real log canonical threshold in a singular one, falling below these where prior or discreteness fixes parameters; with multiplicity above one the approach to the singular value is only logarithmic, and the correspondence has no counterpart of physical current or dissipation | LaMont & Wiggins (2019), LIT-1882, read in NOTE-1481: the learning capacity C = −N²∂_N U and its equipartition values (Table II, eqs. 16–18, 24, 28, 30). Active: the regular entries were checked by differentiation, and the singular case exactly in K = a²b² (CASE-152’s model), where C approaches λ = ½ as ½ − 1/log n, not with the O(1/N) error the paper states. The statistical “temperature” is a sample size, so nothing in the dictionary is a physical heat flow. | Active |
| THEORY-1254 | A controller that must stay safe under every model it has not ruled out cannot use the evidence its committing action produces: if the information it can gather before its first action that forecloses a safe continuation under an alternative is bounded by β, every such controller forfeits at least about ½e^{−β} of the value reachable only by committing, so a linear oracle gap gives linear regret, and acting on an exclusion at risk α needs about log(1/(2α)) nats gathered beforehand | Saligrama (2026), LIT-1880, Theorem 1 and its examples, read in NOTE-1466. The proof is data processing on the stopped record plus Bretagnolle–Huber, and the explicit relaxation and one example’s optimization were checked numerically. Active: a theorem with a short proof, checked. It is a lower bound only; bounded information is sufficient for an unavoidable gap, and unbounded information does not by itself give recovery. | Active |
| THEORY-1255 | Near a non-degenerate minimum, constant-rate SGD’s stationary distribution is a Gaussian set by learning rate, batch size and preconditioner, which can be tuned to match the posterior at a given sample size; training time enters only as the wait for stationarity | Mandt, Hoffman and Blei (2017, LIT-1898; first in 2016, LIT-1899), read in NOTE-1475 and NOTE-1473. Under Gaussian, constant gradient noise BBᵀ, the continuous-time limit and a quadratic loss with positive-definite Hessian A, the stationary covariance solves AΣ + ΣA = (ε/S)BBᵀ; the preconditioner (2S/εN)(BBᵀ)⁻¹ makes it the posterior’s A⁻¹/N exactly. Checked numerically. Active as a result about that model. It does not cover singular posteriors, several basins or the search phase, and it relates the optimiser’s noise scale to sample size, not training time to sample size. | Active |
| THEORY-1256 | When a conservative experiment is safe under every plausible model, can be repeated from a common state and keeps informing, a controller that acts on the lower end of an anytime confidence sequence stays safe with probability 1 − δ and approaches the safe oracle, at O(√(T log T)) regret in a braking example; a certainty-equivalent controller in the same example is unsafe with probability ½ in every episode however much data it has | Saligrama (2026), LIT-1880, §5 (Lemma 5, Theorem 2, Corollaries 5–7, §5.6.1), read in NOTE-1466 with the proofs of Lemma 5 and Theorem 2. Active: a short proof by a Gaussian mixture martingale and Ville’s inequality, checked by hand, and an elementary calculation for certainty equivalence. Narrow: a scalar parameter with a known conservative direction, an experiment that returns to a common state, and Gaussian observations. | Active |
| THEORY-1257 | Averaging constant-rate SGD iterates at stationarity gives a covariance that shrinks with the number of examples processed, and equals the Gaussian posterior’s for that many observations when the noise covariance equals the Hessian | Mandt, Hoffman and Blei (2017), LIT-1898, §6 and App. G, read in NOTE-1475. In their OU model, the mean of T stationary iterates at batch S has covariance A⁻¹BBᵀA⁻¹/(TS) to leading order in 1/(Tελ), whatever the step size or constant preconditioner; under a well-specified regular model (BBᵀ = A) that is A⁻¹/(TS), the Gaussian posterior’s covariance for TS observations. Checked against the exact discrete covariance. It is the one place the paper ties examples processed to a sample size, and it is about spread in one basin after equilibration, not about which region dominates. | Active |
| THEORY-1258 | The steady state of Hennick and De Baerdemacker’s fractional Fokker–Planck model of SGD is a tempered posterior only within a region of constant effective diffusion; the weights between regions, where accessibility would act, are not derived | Hennick and De Baerdemacker (2025; ICLR 2026), LIT-1879, read in NOTE-1467. Their Lemma 3.3 and Corollary 3.2 show that where a scalar effective diffusion D_ξ is constant, the steady state is exp(−L_m/D_ξ), the posterior at effective sample size 1/D_ξ. That is a temperature, and inside such a region it leaves no room for an accessibility correction. Across regions their own equation’s zero-flux state is ∝ exp(−∫∇L/D), set by D along the paths between regions; checked on a double well. Active: the algebra and the counterexample are elementary and checked. It does not say SGD is far from Bayesian across regions, only that the paper does not show it is close. | Active |
| THEORY-1259 | When a teacher’s next-token distribution depends on a context the student cannot observe, the forward-KL-optimal student is the teacher averaged over the contexts compatible with the student’s observation, the loss it cannot remove is the conditional mutual information between the teacher’s output and the hidden context, and the optimal student is at least as uncertain as the teacher is on average; the self-distillation objectives actually trained may not be forward KL at all | Hossain, Kousar and Tourni (2026), LIT-1883, Proposition 1; read in NOTE-1479. Active: elementary and checked numerically. This is the published statement of the limit QUESTION-361 starts from. It holds for the unclipped forward KL; the OPSD objective the paper trains clips each vocabulary entry, which the paper shows reverses the gradient on the teacher’s most preferred tokens. | Active |
| THEORY-1260 | Richens et al.’s sense of “an agent contains a world model” is that the transition function can be computed from the agent’s goal-conditioned input-output map, uniquely to within the theorem’s error, so the attribution is not a stance an observer may withhold, unlike a representation-theorem fit; but it holds of every implementation of the same map, a lookup table included, and so cannot show that a predictive component is realized inside the agent | Richens, Abel, Bellot and Everitt (2025), LIT-1891, read in NOTE-1469. The paper says its recovery map is “from the agent’s policy rather than its activations”, that this is “strictly weaker”, and that it shows “a world model encoded in the agent’s policy, not its specific use”; it contrasts itself with Savage, whose fit exists even for a random policy. That the result applies to Block’s lookup table (LIT-642) is immediate from Def. 5, which constrains only the map. Active: the paper’s own statements plus a one-line corollary. It does not say whether a compact implementation must have a separable predictive part. | Active |
| THEORY-1261 | At stationarity a driven reaction network is confined to a thermodynamic space: each reaction’s affinity lies between zero and the largest cycle affinity per use of that reaction among the elementary flux modes containing it, and each product of concentrations lies between the effective equilibrium constants of the extremal pathways; with no driving the space collapses to the equilibrium point, so multistability, symmetry breaking and amplification above equilibrium need driving and are bounded by it | Liang, De Los Rios and Busiello (2024; PRX 2026), LIT-1886, read in NOTE-1463: eqs. 20, 24 and 29, proved for arbitrary stoichiometry from local detailed balance and the conformal decomposition of steady fluxes into elementary flux modes. Checked on the paper’s Schlögl parameters and on a reversible rewriting of CASE-189. Active. It bounds where a stationary state can be, for every choice of kinetics; it does not say which state is reached, whether it is stable, or how long the driving lasts. | Active |
| THEORY-1262 | In multi-token-prediction pre-training at 167M to 1.2B parameters, the part of the MTP gradient that pulls toward the sampled target carries about four-fifths of the MTP gradient reaching the shared trunk with roughly a quarter of the signal-to-noise ratio of the self-distillation part, and removing it from the trunk improves next-token loss, speculative decoding and zero-shot accuracy by small margins | Teoh (2026), LIT-1896, §6 Figs. 3–4 and Tables 2–6; read in NOTE-1470. Proposed: one run per scale, four scales, no seeds or variances, margins of one to two percent. It does not show that data-anchored correction is dispensable: the output head keeps it, and the paper attributes the explicit-KL variant’s weaker head to its absence there. | Proposed |
| THEORY-1263 | In on-policy self-distillation of language-model reasoning, a privileged-context teacher’s advantage is concentrated on the student’s failed trajectories and is smaller at larger scale, and restricting supervision to the student’s verified trajectories, with the student’s own failed attempt as the teacher’s context, keeps the gain over the base model where standard on-policy self-distillation loses it | Hossain, Kousar and Tourni (2026), LIT-1883, Tables 1, 2 and 5; read in NOTE-1479. Proposed: single training runs, Qwen3 only, the teacher’s advantage measured at two of three scales, and a second candidate cause, per-entry clipping, left in every run. It does not show that the teacher’s privileged knowledge is useless; it shows that it is hard to transmit where the student cannot see what it rests on. | Proposed |
| THEORY-1264 | Far from equilibrium, the weak-noise escape rate from an attractor goes as the exponential of minus system size times a barrier in the quasi-potential, not in any free energy, and that barrier is bracketed by thermodynamics: it is at most the entropy produced in relaxing from the saddle into the attractor and at least minus the entropy produced along the most likely escape path; the two bounds coincide at detailed balance and separate by twice the dissipation of the probability circulation, so far from equilibrium they can be very loose | Santolin, Freitas, Esposito & Falasco (2025), LIT-1881, read in NOTE-1465, for overdamped diffusions; Falasco & Esposito (2025), LIT-1892, §IV.H and appendix A, read in NOTE-1472, for jump processes with a macroscopic limit. Active: the derivation is two lines from the orthogonal decomposition of the drift and was checked on a linear nonequilibrium diffusion. It does not say that the more dissipative state lives longer, and in the one worked far-from-equilibrium chemical example the bracket is very loose. | Active |
| THEORY-1265 | Approximating a chemical master equation by a Fokker–Planck or nonlinear Langevin equation gets the quasi-potential right only at the fixed points: between them it mis-estimates the barriers, so escape rates come out wrong by a factor exponential in system size and the approximation can pick the wrong one of two states as the long-run favourite, and its apparent entropy production vanishes at every steady state, missing the dissipation that sustains it | Falasco & Esposito (2025), LIT-1892, §IV.D–E and §VII.A.1, read in NOTE-1472; Vellela & Qian (2009), LIT-1890, appendix A, read in NOTE-1474. Active: both formulas were checked on the Schlögl model, including Vellela & Qian’s counterexample, where the exact and diffusion quasi-potentials favour different states. It does not say diffusion approximations fail near fixed points or for Gaussian fluctuations; there they are exact to leading order. | Active |
| THEORY-1266 | In an open reaction network of reversible elementary mass-action reactions, sustained currents need an emergent cycle with nonzero affinity: each chemostatted species either breaks a conservation law or opens an emergent cycle, so one chemostat never suffices; with every emergent affinity zero the network relaxes to a unique equilibrium fixed by its unbroken conserved quantities; and a nonequilibrium steady state dissipates exactly the sum over emergent cycles of current times affinity | Rao and Esposito (2016), LIT-1889, read in NOTE-1464, with the one-chemostat proof of Dal Cengio, Lecomte and Polettini (2023), LIT-1897 (NOTE-1476). Active: rank–nullity, Wegscheider’s condition and two lines of algebra, checked numerically on a reversible rewriting of CASE-189’s first construction, which has a single equilibrium at zero affinity and is bistable only above 3.52 RT. It does not say that a driven network is far from equilibrium, multistable or organized; only that without an emergent affinity it cannot be, and what it costs when it is. | Active |
| THEORY-1267 | A safe set that a nominal barrier-function controller keeps invariant can be left under an arbitrarily small input disturbance, but if the barrier inequality holds with a disturbance penalty, ḣ ≥ −α(h) − ι(‖d‖), the state stays in a larger set {h + γ(‖d‖∞) ≥ 0} with γ class-K, and adding a damping term along the barrier’s input direction to any barrier controller gives this with an enlargement of ‖d‖²/(4ε) in units of h | Kolathaya and Ames (2019), LIT-1893, Theorems 1–2 and Examples 1–2, read in NOTE-1477. Short proofs, checked by hand, and both examples checked by simulation. Active. Matched input disturbances only, local, and the enlargement is in barrier units and quadratic in the universal construction, not proportional to the disturbance. | Active |
| THEORY-1268 | In a nonequilibrium steady state of a thermodynamically consistent Markov jump network, the entropy produced while a current is counted, times the squared relative uncertainty of that count, is at least 2k_B, independent of the counting time, so a current precise to ε costs at least 2k_BT/ε² of dissipation; the 2015 letter proves this within linear response and for single-cycle networks at any affinity, and for many-cycle networks far from equilibrium shows it numerically and states it as a conjecture | Barato & Seifert (2015), LIT-1885, read in full in NOTE-1480. Active for the scope stated in the title: the biased walk, the unicyclic formula (A/N) coth(A/2N) and the bound on random four-state networks were checked numerically. It bounds the precision of currents, not of occupations, so it does not price how long a maintained state lasts, and the general multicyclic proof is not in this paper. | Active |
| THEORY-1269 | In overparameterized linear regression, iterated self-training with fresh covariates, noiseless pseudo-labels and minimum-norm students applies a fresh random orthogonal projection to the estimate each round, so noise from the first fit decays geometrically while signal along a direction of variance s decays at the slower rate s/(s + τ); risk is U-shaped under anisotropy and monotone under isotropy, tends to the risk of predicting zero, and every student fits its teacher exactly on its own sample | Wu, Yang and Sun (2026), LIT-1884, Theorem 3.2, Corollaries 3.3–3.4 and B.1, and the projection identity of §3.2; read in NOTE-1471 and checked by Monte Carlo in the spiked model. Active for the spiked closed form; the general concentration result (Theorem 4.2) is the paper’s, proof not checked. It does not cover reused data, noise injected every round, or nonlinear students. | Active |
| THEORY-1270 | Entropy production does not select which of several maintained steady states is the stable one: in the bistable Schlögl model the state the system occupies in the long run can carry either the higher or the lower deterministic entropy production rate, and the mean stochastic entropy production follows whichever state is more probable; in general the most dissipative attractor is the longest-lived only under special conditions, and lifetime tracks relaxation entropy only near detailed balance | Vellela & Qian (2009), LIT-1890 (§3.3, Fig. 6), read in NOTE-1474, show the counterexample; Falasco & Esposito (2025), LIT-1892 (§§III.F, IV.H, VIII.B.6), read in NOTE-1472, give the general account: minimum entropy production holds only near detailed balance with linear dynamics, and the two maximum principles hold only where relaxation and escape dissipations nearly coincide. Active as a negative result. It does not refute every extremum principle, only those that rank steady states by dissipation alone. | Active |
| THEORY-1271 | Mossio, Montévil and Longo argue that closure of constraints both stabilizes and propagates variation: it regenerates each constraint beyond the time scale at which it is conserved, and removes a variation only if the variation does not reach the constraints that regenerate the varied one; when it does reach them, the variation propagates and the system either loses closure and disintegrates or comes to realize a new closure, which they say a rock, a flame or a table cannot do | Mossio, Montévil and Longo (2016), LIT-1888, §5, read in NOTE-1461. The conditional is close to definitional. That regeneration actually recovers is a dynamical claim the paper does not model, and the contrast with non-organized systems rests on three examples. Proposed. It does not say how large a variation closure can absorb, nor that recovery follows whenever the structural condition holds. | Proposed |
| THEORY-1272 | Late in training, SGD weights drift sub-diffusively, with displacement growing as a power of training time set by a spectral dimension and the local learning coefficient | Hennick and De Baerdemacker (2025; ICLR 2026), LIT-1879, read in NOTE-1467. Late-training displacement fits R(t) ∝ t^α with α below ½ on MNIST MLPs, TinyStories models and ImageNet convnets fine-tuned with SGD, read through the Alexander–Orbach relation as α = d_s/(2λ) with d_s ≤ λ. Proposed: d_s is obtained by fitting that same relation, so the fits test the power law and not its link to the LLC; Kunin et al. report super-diffusion in another regime. | Proposed |
| THEORY-1273 | In a driven chemical system with two stable states and a finite number of molecules, each maintained state is metastable: it is left by fluctuation after a time exponential in system size, set by a barrier in a nonequilibrium quasi-potential that closes at the saddle-node, and the long-run share of time in each state is fixed by the parameters and system size, not by the initial condition; the deterministic rate equation, where the initial condition decides, holds only on times short of that escape time | Vellela & Qian (2009), LIT-1890, read in NOTE-1474, on the Schlögl model, with Falasco & Esposito’s general frame (LIT-1892, §§III.C, IV.H, VI; NOTE-1472). Active: the slow eigenvalue, the barriers, the initial-condition independence and the closing of the barrier at the fold were checked numerically on the paper’s model. It does not say which state is the more stable without computing the quasi-potential, and the paper’s own large-volume rate formula carries a spurious 1/V factor. | Active |
| THEORY-1274 | Under a shared linear output head, the cross-entropy gradient of a multi-token-prediction head at its hidden state is exactly the gradient of a forward KL toward the model’s own position-aligned next-token prediction, held fixed, plus the next-token cross-entropy gradient at the aligned state, which alone carries the sampled target; the identity is about gradients and computations, not information, and in heads fed the intervening tokens the student and its teacher condition on the same evidence | Teoh (2026), LIT-1896, eqs. 1–3 and Appendix B; read in NOTE-1470 and checked by finite differences. Active: elementary and checked. It is a gradient identity, not a decomposition of the loss’s value, and it does not by itself make the self-distillation a projection onto less information: in the DeepSeek-style heads of the paper’s main results the student sees the same tokens as its teacher. | Active |
| THEORY-1275 | In the toy model of superposition, SGD’s transitions have Bayesian counterparts whose critical sample sizes rise in the order training meets them, yet SGD was not seen to take the posterior’s main transition and ends in a phase the posterior has left at the training sample size | Chen, Lau, Mendel, Wei and Murfet (2023), LIT-1894, read in NOTE-1462. Their Bayesian antecedent hypothesis is one-way: training’s transitions have Bayesian counterparts. From their numbers the antecedents of the chain 4⁺⁺⁻ → 4⁺ → 5 → 5⁺ fall at n ≈ 190, 370 and 1,600–2,500, rising with training. But the posterior’s transition 5 → 6 at n ≈ 600 was not seen in training, and SGD on 1000 samples ends at the 5- or 5⁺-gon while the posterior at n = 1000 favours the 6-gon. Proposed: one model, one SGD setting, estimated learning coefficients. | Proposed |
| THEORY-1276 | In Simondon’s ontology, as his organization-studies readers take it, information is not a signal transmitted between finished entities but a disparity between two differently ordered domains of a metastable system, and its meaning is the new structure that transduction produces in resolving it | Iliadis (2013), LIT-1911, read in NOTE-1485, with Bencherki & Iliadis (2021), LIT-1922. The reading of Simondon on which Bencherki, Brummans & Vézy (2024) build their account of communication and meaning. Proposed: both sources are exegesis in their authors’ translations, and Simondon’s text could not be checked. It does not say that information has no quantitative sense, or that meaning can be identified before the resolution occurs. | Proposed |
| THEORY-1277 | Persons and organizations can be described not as successive stages, with the collective built up from individuals, but as coexisting levels of ordering through which one action propagates, each preserving its components; on that description the problem of scaling up from individual to organizational action does not arise | Bencherki & Iliadis (2021), LIT-1922, read in NOTE-1483, with Bencherki (2017), LIT-1901. The claim behind the parent paper’s dissolution of the scaling-up problem (LIT-1902, p. 1364). Proposed: a conceptual proposal, illustrated by one meeting excerpt, with no criterion that fixes a level independently of the analyst. It redescribes the problem; it does not show that aggregation never occurs. | Proposed |
| THEORY-1278 | Communication can be treated as transduction, the continuity of an action through processes that it transforms, rather than as exchange between parties; meaning is then the contribution an action makes, in retrospect, to a joint individuation, coexisting meanings mark concurrent individuations, and the problem of scaling agency from individual to collective is claimed to dissolve | Bencherki, Brummans and Vézy (2024), LIT-1902, read in NOTE-1484, pp. 1355–1358 and 1363–1365. Simondon’s transduction made into a theory of organizational communication. Proposed: argued from examples, with the dissolution of scaling up asserted. The examples (a synapse, a hunger pang, a piston) show the notion applies to any change, which is its strength as a vocabulary and its weakness as a theory. | Proposed |
| THEORY-1279 | Organizational categories are radially structured, so applying them to nonprototypical cases extends and changes them; this is one source of continuous change in routine organizational action | Tsoukas & Chia (2002), LIT-1913, pp. 573–575, read in NOTE-1489. The paper’s mechanism for organizational becoming, built on Lakoff’s and Johnson’s prototype theory and Hart’s penumbra of legal rules. Proposed: it is supported by illustrative cases, not tested. | Proposed |
| THEORY-1280 | Agency can be redescribed without agents, as the affective force by which one individuation process takes up another’s excess action in a communicative event and both pass from a lesser to an augmented ability to act; agents are then effects of such events, and the absence of the force is disindividuation | Bencherki, Brummans and Vézy (2024), LIT-1902, read in NOTE-1484, pp. 1349–1357. The paper’s central proposal, after the Spinozan formula for affect that Massumi offers as a proposition, not a definition, and Simondon’s individuation. Proposed: argued, and illustrated by one reanalysed meeting. It has no criterion that would let an observation count against it, and it builds the augmenting direction into the definition of agency. | Proposed |
| THEORY-1281 | Montréal School CCO’s commitment to interaction as the basis of organizing makes conversation analysis its method of choice, and that commitment keeps ventriloquism from serving as an open metamodel for communication theory | Wilhoit (2016), LIT-1923, read in NOTE-1487. An argument about method in a five-page reply to Cooren. It is not a claim that ventriloquial analyses entify agents, which is what Bencherki, Brummans & Vézy (LIT-1902, pp. 1363–1364) cite it for. | Proposed |
| THEORY-1282 | Affect, in Massumi’s sense, is the felt transition of a body’s power to affect and be affected toward a diminished or augmented capacitation, offered as a proposition to be regenerated in each use rather than a definition to apply | Massumi (2009), LIT-1905, read in NOTE-1488, p. 1; reprinted in Politics of Affect (2015, pp. 47–48), LIT-1907. The definition is Spinoza’s as Deleuze took it up, and it runs both ways, diminished or augmented. Massumi says it is “not a general definition that you can apply”. Bencherki et al. (LIT-1902) quote it exactly and then apply only its augmenting half, as a definition of agency. | Proposed |
| THEORY-1283 | Micropolitics is the modulation of a relational field toward a maximally inclusive co-patterning of contrasting tendencies, in which each realizes itself without curtailing the others; the co-patterning is aesthetic, an affirmation of discord rather than its resolution | Massumi (2017), LIT-1910, p. 64, read in NOTE-1486; anticipated in the 2009 interview (LIT-1905, p. 12) as “a symbiosis: a cross-fertilization of capacitations”. It is an aim, which Massumi grants “sounds utopic” and calls “always-as-yet unknowable”. Bencherki et al. (LIT-1902, p. 1358) quote it exactly and use it to say what organizational becoming is constituted by. | Proposed |
| THEORY-1284 | Organization is a secondary accomplishment of change: change in organizations is continuous, as actors reweave their webs of beliefs and habits to accommodate new experience, and organization is both the attempt to stabilize that flux and the pattern that emerges from it | Tsoukas & Chia (2002), LIT-1913, read in NOTE-1489. The thesis of organizational becoming, which Bencherki, Brummans & Vézy 2024 (LIT-1902) say their theory parallels. Proposed: it is argued from process philosophy and illustrated from others’ ethnographies. The change it describes is carried by human actors, not agent-free. | Proposed |
| THEORY-1285 | Organizational action can be described as pre-individual, so that whose action it is, a person’s or an organization’s, is an outcome of the individuations it is allowed to contribute to rather than a given; an action then has as many significations as the individuations it takes part in, and a person whose action is refused a collective’s recognition experiences that as disindividuation | Bencherki (2017), LIT-1901, read in NOTE-1482, with Bencherki & Iliadis (2021), LIT-1922. The proposal of which Bencherki, Brummans & Vézy’s “agency without agents” (LIT-1902) is a development. Proposed: argued, and illustrated by three excerpts from one documentary. Nothing identifies disindividuation apart from the affect it is inferred from, and the account needs, but disclaims, a standard of whose action it rightly was. | Proposed |
| THEORY-1286 | Affect is not transmitted from one body or event to another; it is reactivated anew in each event, and bodies cued by the same event are attuned to it differentially rather than made alike | Massumi (2009), LIT-1905, read in NOTE-1488, pp. 6 and 9: affect “is not a content that can be transported from one event to another … an event logic, not a logic of transmission or communication”, and there is “affective difference in the same event”. This sits uneasily with the “excess action” that Bencherki et al. (LIT-1902) have passing between individuation processes. | Proposed |
| THEORY-1287 | The experiments mechanists use to find a mechanism’s components (correlation, lesion, stimulation, and intervening on the whole while recording the parts) run in both directions between part and whole and, by Craver and Bechtel’s own account, show only prima facie that an item is a component, because an item not interactively integrated into the system could be a background condition; they give no test of integration, so the experiments do not by themselves fix where a mechanism ends | Craver and Bechtel (2007), LIT-1928, pp. 553–554, read in NOTE-1491. The four kinds of interlevel experiment “share a form with Mill’s methods” and are symmetrical. A lesion deficit is “only prima facie” evidence of componency, since a part “not interactively integrated” may be a background condition (n. 10). “Integrated” is never defined, and nothing in the four experiments tests where the system’s edge is. That leaves the mechanism’s boundary to be fixed some other way. | Active |
| THEORY-1288 | If a mechanism’s behaviour supervenes on its constituents’ behaviours and constitution is not causal, every cause of that behaviour is also a cause of some constituent along another path, so no intervention can change the whole without separately changing a part; mutual manipulability by ideal interventions is then unsatisfiable, and once interventions are relaxed to admit these common causes, every model with constitutive dependence has a model without it that implies the same correlations under every manipulation, even in ideal experimental conditions | Baumgartner & Gebharter (2016), LIT-1934, pp. 10–13, 18–20, and Baumgartner & Casini (2017), LIT-1939, pp. 6–11; restated by Baumgartner, Casini & Krickel (2020) as Systematic Fat-Handedness. Read in NOTE-1493 and NOTE-1490. Active as a conditional: valid on supervenience and non-causal constitution, and checked step by step. It does not say that constitution cannot be known, only that no finite set of manipulations of whole and part shows it; and it is about simultaneous whole–part dependence, not about a diachronic cause inside a system, which can be intervened on surgically. | Active |
| THEORY-1289 | In a dynamical model anchored to an identified mechanism, holding one part’s variable fixed and finding that the phenomenon persists indicates that the part is not a component of the mechanism responsible for that phenomenon, as when Smolen et al. fixed CLOCK and circadian oscillation continued; the verdict is relative to the phenomenon and only as good as the model, and it decides which pathways the phenomenon needs, not which lie inside the system | Bechtel and Abrahamsen (2010), LIT-1936, contribution C3 (p. 326), read in NOTE-1492. Smolen et al. (2001) fixed the concentration of CLOCK in a reduced model of the Drosophila clock, and oscillation continued. They concluded that the positive CLOCK loop “was not critical”. That is a part that belongs to the system and not to “the responsible mechanism for that particular phenomenon”. The clamp is an ideal intervention, cheap in a model and hard in vivo. It is not a test of where the system’s boundary lies. | Active |
| THEORY-1290 | A dynamical model whose variables are properties of parts and operations already identified by experiment explores the dynamics of that mechanism, while one that posits its parts de novo and is checked only by fit to behaviour shows at most how a mechanism of that kind could produce the behaviour; fit can rule such models out but usually cannot decide between competing architectures that each fit, and what decides is independent evidence about the parts | Bechtel and Abrahamsen (2010), LIT-1936, read in NOTE-1492. Circadian models came after the clock’s parts were found in the laboratory, and they explore those parts’ dynamics. Cognitive models posit their parts. “Empirical evidence can rule out specific models, but usually cannot decide between competing architectures” (p. 332). It does not say de novo models are worthless: they make the same six kinds of contribution, at weaker standing. Nor does it say that anchoring makes a model right. | Active |
| THEORY-1291 | Within levels of mechanisms, apparent top-down and bottom-up causes can be read as mechanistically mediated effects, intralevel causation among components together with the constitution of the whole by them, so that the relation between levels is constitution and not causation; Craver and Bechtel show the translation for six cases, on the assumption, not argued, that every higher-level cause has a mechanistic explanation | Craver and Bechtel (2007), LIT-1928, read in NOTE-1491. Parts and wholes are not distinct events. So, given transmission, distinctness or asymmetry views of causation, they cannot be cause and effect, and the symmetry of interlevel experiments is explained by constitution. The six worked cases translate. The account says nothing about whether a feedback loop crossing the mechanism’s boundary changes the analysis, and its generality is assumed. | Proposed |
| THEORY-1292 | Whether a coupled oscillator sustains its own rhythm or is a damped oscillator driven from outside is settled directly by removing the drive, and, because the two arrangements are not dynamically equivalent, may also show in how they respond to a shift of phase: in Leise and Siegelmann’s model, damped peripheral clocks regain their phase relation to the central clock quickly, while self-sustained ones take longer, need strong coupling, and sometimes resynchronize by a long delay instead of an advance | Bechtel and Abrahamsen (2010), LIT-1936, §3.6, p. 328, read in NOTE-1492. Peripheral clocks were once taken for “slaves” of the SCN, damping without it. Later evidence suggested they keep oscillating and lose synchrony, so the SCN is “a conductor” rather than “a ringmaster”. The paper’s reading is that models of both kinds “can reveal the empirical signatures that each may leave”. This is a biological instance of the record’s question where maintenance is realized. It is also a case outside CLAIM-522’s ideal limit: the outside drive does not reproduce the inside law, so a perturbation of state may tell them apart. | Proposed |
| THEORY-1293 | Given that every change in a phenomenon is simultaneously realized by some constituent on every lower level, that simultaneous changes are not causally related, that co-occurrence is transitive, and that the parts and their levels are already known, a single intervention that changes a part and the phenomenon simultaneously while directly changing at most one behaviour on each lower level shows that the part is a constituent; the condition presupposes the boundary and the level hierarchy it is applied to and cannot supply them | Baumgartner, Casini & Krickel (2020), LIT-1924, §§3–4, read in NOTE-1494. Active as a conditional: the eight-line reductio is valid on Universal Constitution, Simultaneity and transitivity of co-occurrence, and checked. It does not say such interventions exist in any real system, that the condition is necessary, or where the boundary lies; and its line between causation and constitution is simultaneity, which is sharp only at a fixed time resolution. | Active |
| THEORY-1294 | Constitution is best inferred, and only abductively, from the failure to break a coupling: a set of parts constitutes a phenomenon when every cause of the phenomenon is also a cause of some member of the set, no smaller set does as much, and no expansion of the variables studied turns up a cause of the phenomenon that spares them all, so constitutive relevance is fixed by the set a part belongs to and no finite series of experiments settles it | Baumgartner & Casini (2017), LIT-1939, §§4–5, their No De-Coupling account, developing the fat-handedness criterion of Baumgartner & Gebharter (2016), LIT-1934, pp. 20–22. Read in NOTE-1490 and NOTE-1493. Proposed: a definition offered with no operationalization and no case from practice, which the authors say themselves. It does not say how far a variable set must be expanded, and it takes parthood as given. | Proposed |
| THEORY-1295 | Metzinger 2024 calls consciousness without an egoic self or first-person perspective “empirically established” on the strength of retrospective, self-selected reports from meditators, while its own methods chapter grants that a remembered report of a selfless state is “highly dubious” evidence that the state was selfless when it occurred, and leaves that problem open | Metzinger (2024), LIT-1943, read in part in NOTE-1499. The summary chapter says that “full-absorption episodes, nonegoic self-awareness, and nondual modes of consciousness are empirically established phenomena” (p. 457), and that the strong reading of subjectivity “is false” (p. 459). The methods chapter grants self-selection, theory contamination, unreliable recall and, at p. 19, that reports of having been selfless are “highly dubious from a methodological perspective” because autobiographical memory represents events as a self’s. It calls the question “open”. Active: the two passages are read and quoted. Whether selfless consciousness occurs is not settled either way here. | Active |
| THEORY-1296 | Deliberate thought selects and sustains candidates from a stream of unintended thoughts that mind-wandering generates, and whether the conscious model of oneself as a knower that accompanies the selection causes it, enables it or only accompanies it is undecided by current evidence | Metzinger (2017), LIT-1945, pp. 11–17, read in NOTE-1496. The “cognitive affordance hypothesis”: mind-wandering is “mental sleep-walking” that “sets up the inner world” of candidate mental actions, and frontal control “latch[es] onto the best candidate”. Offered as a hypothesis after Clark and Cisek’s affordance competition, with no data. The second clause is the chapter’s own statement that the data “do not help to decide” what the epistemic agent model does, which takes back the principle the 2015 paper stated. “Best” is not defined, so the hypothesis does not say whether selection is by the candidates’ content or by relations that govern them. | Proposed |
| THEORY-1297 | Mind-wandering is a recurring loss of M-autonomy, the veto-centred ability to suspend or end one’s own ongoing mental processes; on the figures Metzinger uses, it takes about half of conscious time, not the two thirds he states | Metzinger (2013), LIT-1942, restated in 2015, LIT-1941; read in NOTE-1495 and NOTE-1497. The identification is conceptual: an episode of unintentional mind-wandering cannot, while it runs, be suspended or ended at will, and veto is what M-autonomy turns on. The share is computed from others’ figures, and recomputed here: 631 of 1207 conscious minutes, 52%, against the “roughly two thirds” both papers state. Proposed: no measure of veto during episodes is reported, and the 30–50% figures count task-unrelated thought, which includes deliberate daydreaming the definition excludes. | Proposed |
| THEORY-1298 | When mental control returns after mind-wandering, the self-model represents the return as the person’s own act whether or not the person’s control system caused it, because it must bridge to earlier control to keep the autobiographical self-model continuous | Metzinger (2015), LIT-1941, pp. 289–292, read in NOTE-1497; first in 2013 (LIT-1942, pp. 4, 11) and widened in 2017 (LIT-1945, pp. 20–21) to the sense of origination in agency generally. It rests on Schooler et al. (2011) and Wegner (2002), neither read, and on the argument that a self-model which must represent itself as always having had the ability cannot represent its return as caused from outside. A hypothesis: no episode is reported in which the cause of a return and the report of it were recorded apart. | Proposed |
| THEORY-1299 | Pure awareness, on Metzinger’s account, is the content of a temporally thin model of the organism’s own tonic alertness, its capacity to know; experience in this minimal form lacks an egoic self-model, a first-person perspective, time, space and even phenomenal oneness, but not self-modelling, and tonic alertness that is not so modelled is not experienced | Metzinger (2020), LIT-1946, read in full in NOTE-1498, and Metzinger (2024), LIT-1943, skimmed in NOTE-1499. MPE is “an inner representation of tonic alertness”, “non-egoic self-modelling” that “definitely has representational content”. In the 2024 sketch it is “a highest-level but nonegoic self-model” of the system’s epistemic openness, which “really endows the content generated on all lower-order levels with phenomenality”. It is a hypothesis fitted to retrospective reports. It does not say that consciousness needs no model of the system, only that it needs no model of a knowing self. | Proposed |
| THEORY-1300 | In mind-wandering the capacity for veto over one’s own mental processes is kept and its representation in the self-model is lost, and on Metzinger’s principle a capacity can be deliberately exercised only while it is so represented; the loss of M-autonomy is then the loss of a condition of the capacity’s efficacy, not of the capacity | Metzinger (2015), LIT-1941, pp. 280–283 and 296, read in NOTE-1497; anticipated in 2013 (LIT-1942, p. 3, note 4). The “moderate, nuanced position”: what is lost is “not the ability itself” but “conscious knowledge of our potential for second-order mental action”, with the “principle of ‘Autonomy by Phenomenal Self-Representation’”. Both are stated, not argued, and neither is tested. Metzinger’s 2017 chapter (LIT-1945, pp. 13–14) says the data cannot decide whether the self-model constitutes, enables or only accompanies control, which withholds the principle’s causal reading. “Deliberately” also does work: inhibition can be wholly subpersonal. | Proposed |
| THEORY-1301 | In the Haken–Kelso–Bunz potential V(φ) = −a cos φ − b cos 2φ, switching the parameters in time from no landscape (a = b = 0) to two wells (a = b = 1) to one well (a = 1, b = 0) makes the spread of the relative phase across trials rise while both wells are open and fall after one is removed, the pattern Sánchez-Cañizares compares qualitatively with post-stimulus quenching of trial-to-trial variability in decision tasks; under Gaussian white noise of the stated strength q = 1 the spread of cos φ settles near 0.40, not at 0 | Sánchez-Cañizares (2026), LIT-1992, read in full in NOTE-1506 from the publisher’s open-access PDF. Active for the model’s behaviour, which this reading checked: the bistability condition |a| < 4b analytically, and the rise and fall by re-simulation (20,000 paths). The paper’s statement that the spread decreases “to 0” holds without noise and fails at q = 1. It does not say that the model fits the cited EEG data, which the author calls “only qualitative”, or that the parameter changes are the mind’s (THEORY-1302). | Active |
| THEORY-1302 | Sánchez-Cañizares reinterprets Irruption Theory for binary decisions (IAT*): irruption is the onset of a landscape with one attractor per option and absorption the passage to a single attractor, both correlated in mind and brain, reversing the sign of Froese’s variance hypothesis; the mind’s causal role is to set the landscape’s control parameters by “selecting the relevant physical coarse-graining”, not to push the state, so on this account the mind controls which outcomes exist and not which one the state reaches | Sánchez-Cañizares (2026), LIT-1992, read in full in NOTE-1506. The interpretation is the paper’s (pp. 6–7, 18–20); the last clause is this reading’s description of the control architecture it implies, from the model and simulation of pp. 8–12, in which the choice between wells is settled by initial condition and noise. Proposed: the paper says IAT* “cannot be tested with empirical results without further assumptions” (p. 7). Bears on CLAIM-533 and QUESTION-071. | Proposed |
| THEORY-1303 | For an uncertain linear program, a decision fixed before the data are revealed must satisfy every realization at once (the robust counterpart, ∃ solution ∀ data), while a decision that may adjust after them need only have a feasible adjustment for each (the adjustable robust counterpart, ∀ data ∃ adjustment); the second is never more conservative and can be feasible where the first is not, the two coincide when each constraint’s uncertainty is its own, and decisions may be restricted between them by what part of the data they read or by the form of the rule | Ben-Tal, Goryashko, Guslitzer and Nemirovski (2004), LIT-1975, read in NOTE-1503. Active: the definitions, the two worked examples (checked by hand), Theorem 2.1 and its proof, and the reported inventory results with their sizes. It does not say the information-basis case is solved in general (the paper asserts it extends), nor that affine rules lose nothing. | Active |
| THEORY-1304 | In latent Dirichlet allocation each document draws its own topic mixture from a Dirichlet shared across the corpus and draws a topic afresh for every word, a three-level model of conditionally independent assignments; the mixture of unigrams, which draws one topic per document, is its two-level comparison, and the Dirichlet is a distribution over mixtures, not over topics | Blei, Ng and Jordan (2003), LIT-1948, read in full in NOTE-1519. Active as a statement of the model’s structure, which is definitional and is stated in the text (pp. 996–1001); the variational updates were checked against Appendix A. It does not say LDA fits text well, which rests on perplexity on two corpora, or that its topics are anything beyond devices for representing word distributions, which the authors disclaim. | Active |
| THEORY-1305 | In Kasser and Ryan’s two cross-sectional samples, holding constant how much a person aspires to overall, the relative importance of extrinsic aspirations (money, fame, image) goes with less self-actualization and vitality and more physical symptoms, and of intrinsic aspirations (growth, relationships, community, health) with the reverse; the paper does not test whether this survives the reasons for pursuing the goals | Kasser and Ryan (1996), LIT-1977, read in NOTE-1525 from the scan on the SDT site. Active as a careful reading of reported associations with their sizes and samples: 100 community adults and 192 students, all self-report. The intrinsic and extrinsic results are nearly one contrast, since both enter after an overall score averaged across all seven domains. Not shown: causation, need satisfaction as mediator, or that the pattern holds once the autonomy of one’s reasons is controlled, which the paper names as an open question. | Active |
| THEORY-1306 | In hierarchically organized systems, levels are demarcated by sharp discontinuities in characteristic process and relaxation rates, the embedding level being slower than its components, and a level controls another by constraint only while their rates stay separated: when the cycling rates converge, the control asymmetry and the distinction between the levels are lost, whatever the signal amplitude; Juarrero’s statement of Salthe’s and Allen and Starr’s hierarchy theory | Juarrero (2023), LIT-1995, ch. 12 (pp. 183–191) with ch. 6 (pp. 68, 72, 77), read in NOTE-1532. A philosophical statement of hierarchy theory, quoting Salthe 1985 and Allen, O’Neill and Hoekstra 1984, with examples from academic administration and tumours; no model. Proposed: the rate-demarcation of levels is the hierarchy theorists’, and the loss of control when rates converge is asserted, not shown. It is the closest prior art the record holds for CLAIM-478. | Proposed |
| THEORY-1307 | In Slemp et al.’s meta-analysis of 881 mostly cross-sectional samples, perceived support for autonomy, competence and relatedness each correlated strongly with satisfaction of all three needs (ρ = .44–.62) and negatively with their frustration, but the three supports intercorrelated .67–.71, and their need-specificity appears only in joint models: with all three entered, relatedness support carried relatedness satisfaction (β = .56) and autonomy support added nothing to it (β = .007) | Slemp et al. (2024), LIT-1969, read in NOTE-1507 from the CC BY Online First PDF. Active as a statement of what the meta-analysis reports, its Table 2 reproduced from its Table 1 matrix. It is a statement about correlations, which the authors interpret as effects on theoretical grounds only; it does not say support causes need satisfaction, or that the needs are distinct in the world. | Active |
| THEORY-1308 | In Chen et al.’s student samples from Belgium, China, the USA and Peru, need satisfaction related to life satisfaction and vitality and need frustration to depressive symptoms with no detectable difference across countries, and neither relation was moderated by how much a person valued or desired the need | Chen et al. (2015), LIT-2000, read in NOTE-1527. Two cross-sectional studies, N = 683 and 1,051. The relations and the null moderations are as reported. Proposed because universality is inferred from failures to reject, with fewer than 150 per country in the test half, and because explicit valuation and desire are the only measures of need strength. | Proposed |
| THEORY-1309 | For a small-noise diffusion the Freidlin–Wentzell quasi-potential equals 2 inf ∫ |b| sin²(θ/2) ds over curves, θ the angle between curve and drift, and the minimizing curve is the path a noise-driven transition follows with probability tending to one; with gradient drift and identity noise that curve runs against the drift, the time-reversed relaxation path, while a far-from-gradient drift, as in the Maier–Stein model above β = 4, makes it depart from the heteroclinic orbit | Heymann and Vanden-Eijnden (2008), LIT-1981, read in part in NOTE-1504 (§§1, 2.1–2.2, 4.1, 5). Active: the geometric formula and the gradient case were re-derived for this reading; the path concentration is Proposition 2.3, whose proof was not read but whose statement is standard Freidlin–Wentzell theory; the Maier–Stein threshold is the paper’s computation agreeing with Maier and Stein’s. It does not say anything at finite noise, or for degenerate noise, which the paper’s ellipticity assumption excludes. | Active |
| THEORY-1310 | In Sheldon, Elliot, Kim and Kasser’s three studies of most satisfying events, self-esteem was as salient as autonomy, competence and relatedness in every sample and the largest unique predictor of event affect balance among ten candidate needs in two of the three US samples (β = .28, .38); the authors, SDT researchers, concluded that there may be four fundamental needs and judged it imprudent to treat self-esteem as an outcome | Sheldon et al. (2001), LIT-1966, read in NOTE-1502 from the scan on selfdeterminationtheory.org. Active as a statement of what the paper reports and concludes, checked against Tables 2–7 and p. 336. It does not say self-esteem is a need: the criteria are self-reports of one remembered event, and the self-esteem items read like well-being, which is QUESTION-369’s problem in miniature. | Active |
| THEORY-1311 | The BPNSFS frustration scales measure low need satisfaction in negatively keyed form, not need frustration in the sense of active thwarting, so the separation of frustration from low satisfaction in BPNSFS data, and frustration’s stronger link to ill-being there, is largely a keying artefact | Murphy et al. (2023), LIT-1978, read in NOTE-1530; Kermavnar et al. (2024), LIT-1988, read in NOTE-1509, adopt it. The item content and the keying structure (THEORY-1316) are shown. That the frustration scales are therefore low satisfaction is the authors’ conclusion, held “probably” and “likely primarily”, and by their own account cannot be decided with data in which keying and construct are confounded. Proposed for that step. | Proposed |
| THEORY-1312 | A phase-amplitude coupling measure can be significant when only one non-sinusoidal rhythm is present, because the rhythm’s harmonics carry amplitude that depends on its own phase; such coupling is confined to bands spanning the rhythm’s harmonics, so a measured coupling is evidence of one rhythm modulating another only after waveform shape is controlled | Donoghue, Schaworonkow and Voytek (2021), LIT-1999, §5 and Fig. 5D–E, read in NOTE-1529 from the PsyArXiv preprint, standing on Kramer et al. 2008 and Cole et al. 2017. Active: checked by a short simulation in which a sharp-peaked 10 Hz wave gave a modulation index of 0.021 between its phase and 25–60 Hz amplitude against 0.0001 for a cosine, and none in a single-harmonic or an 80–250 Hz band. It does not say any particular published PAC is an artefact, nor that broadband coupling far above the harmonics is. | Active |
| THEORY-1313 | In two 7–8B chat models, the shift that finetuning induces along a difference-of-means persona vector correlates with how strongly the finetuned model then expresses that trait, r = 0.76–0.97 across synthetic datasets for evil, sycophancy and hallucination, above cross-trait baselines of 0.34–0.86; the last-prompt-token projection predicts a response’s trait at r = 0.75–0.83 overall but mainly by telling prompt types apart | Chen et al. (2025), LIT-1998, read in NOTE-1524 (main text in full, appendices C.2, G.2 and M). Active as the reported measurements, with their sizes and scope: two models, three main traits, synthetic datasets and an LLM judge. It does not say that persona vectors are the mechanism of persona change, which the authors leave open, or that the method finds personas it was not told to look for. | Active |
| THEORY-1314 | Contextual emergence, on which an emergent phenomenon’s parts are necessary but not sufficient, needs a functional boundary between the phenomenon and its context, without which the context could be folded into the base and the account collapse into weak emergence or global supervenience; and the subject of attention is contextually emergent in this sense, its boundary being the skull, meninges and brain stem, so that its macro-level patterns constrain micro-level activity with a power that is not reducible to the parts and needs neither downward nor circular causation | Jennings (2026), LIT-1963, §§4–6, read in NOTE-1508, with Bishop and Atmanspacher 2006 (LIT-1987) and Bishop, Silberstein and Pexton 2022 (LIT-1993), both unread, for contextual emergence. The boundary condition is the paper’s own addition (fn. 15). Proposed, with a sharp edge: the paper’s reason that the boundary resists micro redescription is that its properties “are macro-level ones” (p. 20), which is the point at issue, and its neural evidence fits weak emergence too. Bears on CLAIM-334, whose supervenience premise it denies. | Proposed |
| THEORY-1315 | As a stochastically forced system approaches a fold bifurcation its dominant eigenvalue goes to zero, so it recovers ever more slowly from small perturbations, and under ongoing perturbation this critical slowing down shows as rising lag-1 autocorrelation and rising variance; skewness and flickering are further warnings not caused by slowing; but the same signals, less pronounced, also precede thresholds that are not bifurcations, so they mark proximity to a broad class of thresholds and not which kind, nor when the shift will come | Scheffer et al. (2009), LIT-1956, read in NOTE-1536 (Skimmed) from the version reprinted as chapter 2 of Dakos’s 2011 thesis. Active for the slowing-down result, which is standard (Wissel 1984), checked in the chapter’s Box 2.2 example, and re-derived and simulated here for variance σ²/(2|λ|) and autocorrelation e^{λΔ} since the chapter’s Box 2.3 was not extractable. The scope and timing caveats are the authors’ (p. 31). It does not say the signals have been shown in chaotic systems, which the review calls “less well studied”, or that any of the reviewed empirical cases was checked here. | Active |
| THEORY-1316 | In eight samples pooled to 3,692 respondents, the covariance of the BPNSFS items is organized more by item keying than by need: factors sharing a keying direction correlate .64 to .75 while satisfaction and frustration of the same need correlate .17 to .38, a higher-order model grouping the six scales by keying fits better than one grouping them by need, and the frustration items carry almost no thwarting content | Murphy et al. (2023), LIT-1978, read in NOTE-1530 from the PMC author manuscript. Active as a statement of what their analyses show, checked against Tables 1–3 and the reported fits: the factor intercorrelations, the two higher-order models and their indices, the external correlates sorted by keying, and the items. It does not say that the frustration scales measure nothing but keying; the authors hold that this cannot be settled with existing data, and the inference is THEORY-1311’s. | Active |
| THEORY-1317 | During held covert spatial attention in human fronto-parietal and visual cortex, the amplitude of broadband high gamma (80–250 Hz) is coupled to the phase of an endogenous 2–5 Hz rhythm, more strongly for the contralateral field, and the trial-by-trial strength of that coupling correlates with faster detection; the evidence is correlational, so it shows that the coupling tracks attention, not that it improves it | Szczepanski et al. (2014), LIT-1982, read in NOTE-1528 from the publisher’s open-access PDF. Active for what it states: the reported counts (123 of 273 electrodes coupled; 55 stronger contralaterally; 28 correlating with RT, r(41) = −0.51 and r(47) = −0.37 in the examples) were checked against the text, and the ERP and power controls are in it. The sharp edge is the causal one: no manipulation of the coupling was made, and the paper’s “facilitate” and Jennings’s “improve” outrun it. | Active |
| THEORY-1318 | Among 31 original self-report scales of psychological need fulfillment found by a 2023 systematic search, 21 measure satisfaction only, one measures frustration only and one thwarting only; all are self-reports of experience or of the perceived environment, the field uses satisfaction, frustration, support and thwarting interchangeably in places, and several frustration scales are negatively worded satisfaction items | Kermavnar, Avsec, Huang and Desmet (2024), LIT-1988, read in NOTE-1509 from the version of record. Active as a statement of what the review counted and found, checked against its §3 and Tables 2–4, within the scope it set (English, healthy general populations, title terms). It does not rank the scales, test their validity, offer a criterion for need-hood, or take a side on the two-dimensional model. | Active |
| THEORY-1319 | In Niemiec, Ryan and Deci’s post-college sample, attaining intrinsic aspirations went with more well-being and less ill-being, and attaining extrinsic aspirations, entered alongside it, added nothing to well-being and went with more ill-being; the extrinsic null is a unique-variance result, since alone extrinsic attainment correlated positively with well-being and need satisfaction | Niemiec, Ryan and Deci (2009), LIT-1960, read in NOTE-1520 from the PMC author manuscript. N = 147 at two years post-college; latent SEM and residualized-change models, all self-report. The intrinsic result and the extrinsic null are as reported; the null holds only with intrinsic attainment in the model. Proposed because one small correlational sample cannot show that extrinsic success fails to raise well-being. | Proposed |
| THEORY-1320 | In Ntoumanis et al.’s meta-analysis of 73 SDT-informed health interventions, mostly randomized, the interventions raised perceived need support (g = 0.64), autonomy and competence satisfaction (0.37, 0.31), autonomous motivation (0.30) and health behaviour (0.45) by the end of the intervention, but not relatedness, controlled motivation or amotivation, and their small effect on psychological health (0.29) was gone at follow-up (0.14, ns); need frustration was not an outcome and mediation was not tested | Ntoumanis et al. (2020; issue 2021), LIT-1962, read in NOTE-1526 from the open-access PDF. Active as a statement of what the meta-analysis reports (Table 1, p. 222), with its sizes, intervals and k. It is the record’s experimental evidence that manipulating need support moves SDT’s proximal constructs; it is not evidence that need frustration is a process in psychopathology (THEORY-052). | Active |
| THEORY-1321 | Froese proposes that irruptions combined with attunement, modelled on Watson et al.’s self-optimization of a Hopfield network by occasional resets to arbitrary states plus Hebbian learning, answer the libertarian’s randomness challenge, how behaviour can be effective though underdetermined; but in the model offered the resets are arbitrary, so what makes the behaviour effective is the learned attractor landscape, and nothing in it distinguishes a motivated irruption from noise | Froese (2023), LIT-1950, read in full in NOTE-1521. The first half is the paper’s proposal (§§4, 5.2.3, 6); the second half is this reading’s observation about the model it cites, from the paper’s own description of it (“reset to an arbitrary configuration”). Proposed because the proposal is stated as potential (“holds potential to provide”) and no model with motivated irruptions is given. It bears directly on CLAIM-533 and on the luck objection (THEORY-328, THEORY-040). | Proposed |
| THEORY-1322 | In Belgian adolescents, need frustration measured by the twelve BPNSFS frustration items statistically absorbs most of the association between depressive and eating disorder symptoms: cross-sectionally their latent correlation falls from .50 to a non-significant .18, and in a two-wave latent change model their correlated change falls from .43 to .24; its mediating role is shown in correlated change over the same six months, not in temporal order | Campbell, Boone, Vansteenkiste and Soenens (2018), LIT-1964, read in NOTE-1533 from the early-view PDF on selfdeterminationtheory.org. Active as a statement of the reported models, checked against the text and Tables 1–2. It is the study THEORY-052 cites through LIT-561 p. 12 as the one longitudinal evidence for need frustration as transdiagnostic. It does not show that frustration precedes the symptoms, does not reach externalizing problems, and its measure is the one THEORY-1311 doubts. | Active |
| THEORY-1323 | Under weak local noise a many-body operator decays at a rate proportional to its size, so a Hamiltonian’s small-sized integrals of motion, which chaotic dynamics does not spread, decay slowly while generic operators, which it spreads, decay fast; in exact diagonalization of Ising and Heisenberg chains of up to nine sites at weak depolarizing noise, the slowest Lindbladian eigenoperators are linear combinations of the known exact and approximate small integrals of motion, and which approximate ones rank among the slowest moves with the noise strength | Yang and Abanin (2025), LIT-1958, read in NOTE-1534. Active as a statement of what the paper derived exactly and what its exact diagonalization showed at the sizes it reached. It does not say that the correspondence holds at large system size (THEORY-1343), that every integral of motion is found (those above size 3–4 are not), or that slowness ranks conserved quantities independently of the environment. | Active |
| THEORY-1324 | In Ryan, Mims and Koestner’s experiment, the same expected reward for doing well left less later free-choice engagement when given with controlling feedback than with informational feedback, and in both styles less than no reward with the same feedback: the interpersonal style of a performance-contingent reward changes its effect, and the reward lowers intrinsic motivation even when the information it carries is held fixed | Ryan, Mims and Koestner (1983), LIT-1970, read in NOTE-1522 from the scan on the SDT site. One experiment, N = 96, n = 16 per cell, ANCOVA on initial interest. The framing effect is F(1, 89) = 4.25 and the reward effect against feedback-matched controls F(1, 89) = 4.34; recomputed from the cell means without the covariate, about 4.9 and 3.4 (p ≈ .07). Felt pressure was higher under controlling conditions; mediation was not tested. Proposed for replication and mediation. | Proposed |
| THEORY-1325 | In Chirkov et al.’s student samples from South Korea, Russia, Turkey and the USA, the more autonomous people’s reasons for engaging in practices of any cultural orientation, collectivist and vertical included, the higher their well-being, with no detectable difference across countries or genders; and vertical practices were much less internalized than horizontal ones | Chirkov, Ryan, Kim and Kaplan (2003), LIT-1989, read in NOTE-1513 from the published PDF on selfdeterminationtheory.org. N = 559, cross-sectional self-report. The positive relation held in every country and for every type of practice (β = .15–.42 within country); “no moderation” is twelve non-significant interactions in samples of 94–195. The primary study for SDT’s claim that autonomy is not individualism, which it supports empirically only in this form. | Proposed |
| THEORY-1326 | In Voigt’s model of hard decisions, when two options are valued equally the value differential is too small to choose (conflict, dACC), and the tie is broken during the choice by fixation: precuneus allocates spatial attention bottom-up to the salient item and dlPFC holds it in working memory, which both settles the choice and raises that item’s value, a change that lasts only if the choice is remembered (hippocampus) | Voigt (2022), LIT-1976, an Opinion article read in NOTE-1517. The model is the author’s “tentative” synthesis, resting mainly on Voigt et al. 2019 (not held) in which fixation duration and dlPFC and precuneus activity predicted later preference change; the causal role of gaze is imported from other studies. Proposed. The sharp edge for its use by Jennings (THEORY-1341): the attentional step is bottom-up capture by salience, not top-down prefrontal feedback. | Proposed |
| THEORY-1327 | As Ryan and colleagues’ 2022 meta-review maps it, the meta-analytic evidence for self-determination theory is concentrated in cognitive evaluation, organismic integration and basic needs theory, is mostly cross-sectional and heterogeneous, and has gaps: no meta-analysis of relationships motivation theory or of need frustration, one or two of causality orientations and goal contents, and none that separates integrated from identified regulation | Ryan, Duineveld, Di Domenico, Ryan, Steward and Bradshaw (2022), LIT-1967, read in NOTE-1500 from the accepted manuscript on OSF. Active as a statement of what the review reports about the 60 meta-analyses it found to July 2021, which is checkable against its Tables 1 and 2 and its own summaries. It does not say the meta-analyses are sound, since the review grades none of them, and it is written by the theory’s co-founder, with several included meta-analyses by its authors. | Active |
| THEORY-1328 | Kane answers the luck objection by making indeterminism a hindrance inside goal-directed effort rather than a cause on its own: in a self-forming action the agent makes two competing efforts, each meeting the indeterminacy as interference from the other, so whichever succeeds is a willed success for which the agent is responsible; indeterminism lessens the agent’s control but not its responsibility, and what responsibility needs is macro-control of processes involving many neurons, not control of each | Kane (2009), LIT-1984, pp. 39–44, read in NOTE-1518. Proposed: the reply rests on analogies whose structure differs from the self-forming case (one aim and an outside obstacle against two aims, each the other’s obstacle), and it does not meet the rollback form of the luck objection (THEORY-328 is the record’s nearest neighbour). Its concession, that indeterminism lessens control, is what CLAIM-533 turns on. | Proposed |
| THEORY-1329 | On Kane’s account, self-forming actions occur under motivational conflict, when tension moves the relevant brain regions away from thermodynamic equilibrium, “a kind of stirring up of chaos” that makes them sensitive to micro-indeterminacy at the neuronal level, so that the choice is undetermined | Kane (2009), LIT-1984, p. 39, read in NOTE-1518. Kane’s neural hypothesis, stated without evidence in this paper. Proposed: it is an empirical claim about brains for which the paper gives none, and the record holds nothing that measures it. It is the attribution CLAIM-533 makes to Kane, now checked against his text. | Proposed |
| THEORY-1330 | In Gemma 2 27B, Qwen 3 32B and Llama 3.3 70B, activation vectors for 275 prompted character roles span a low-dimensional space whose first principal component runs from fantastical to Assistant-like roles, with role loadings correlated above 0.92 between models and the default Assistant at its extreme; the contrast vector from the default Assistant to the role mean aligns with it and is largely present before post-training | Lu et al. (2026), LIT-1991, main text read in NOTE-1505. Active as the reported geometry, with its sizes: three open-weight models, judge-filtered role vectors at one layer, base-model evidence from one model’s PCs and two models’ steering. It does not say the Assistant is a single direction (the authors call the linear assumption “likely flawed”), nor that the axis’s meaning beyond its ends is settled. | Active |
| THEORY-1331 | Deci and Ryan’s General Causality Orientations Scale measures autonomy, control and impersonal orientations as three separately scored and largely independent dispositions, reliable and stable over two months, whose validity rests on correlations with self-report measures in small samples, with behaviour its weakest support | Deci and Ryan (1985), LIT-1955, read in NOTE-1531 from the scan on the SDT site. Active as a statement of what the scale is and what its founding paper showed: α .69–.74 and near-independent subscales in 636 students, retest .71–.78 in 51, and a nomological table in samples of 42 to 87. It does not say that orientations cause behaviour, or that the orientations parallel the three kinds of event of cognitive evaluation theory, which the paper asserts and its data only suggest. | Active |
| THEORY-1332 | In Bishop’s account, chaos is a property of deterministic dynamics, so sensitive dependence is not indeterminism; under determinism it may model deliberation but is not sufficient for incompatibilist freedom, and under indeterminism the incompatibilist (Kane) must still show that agents can harness amplified indeterminism; and amplification itself may fail, since damping, the sign of the local Lyapunov exponents when a perturbation arrives, and the brain’s parallel redundancy limit it | Bishop, SEP “Chaos” (2008; revision of 2024-10-11), LIT-1961, §§4, 6.1 and 6.4, read in NOTE-1535. Active as a statement of the entry’s position, checked verbatim, and its §4 dynamics is elementary. The sharp edge: the brain-redundancy point is asserted without evidence, and the entry does not argue that harnessing is impossible, only that it has not been shown. | Active |
| THEORY-1333 | Bishop’s contextual emergence, as stated in his 2024 SEP revision, is an ontological account: stability conditions not given at smaller and faster scales (parameter values, dimensionality, large-scale flows) constrain or enable what is possible and actual at those scales, as convection rolls constrain the motions of fluid molecules, without the brute new causal powers of strong emergence; laws bound possibility and contexts fix actualization | Bishop, SEP “Chaos” (revision of 2024-10-11), LIT-1961, §§6.2–6.3, read in NOTE-1535, summarizing Bishop, Silberstein and Pexton 2022 (LIT-1993, not reached). Active as a statement of the view, checked verbatim. It corrects the record’s gloss (THEORY-1314, NOTE-1508) that Bishop’s contextual emergence concerns only the well-definedness of a higher-level description; it is not evidence that the view is true, and it sets the view against causal powers, not for them. | Active |
| THEORY-1334 | Persona shifts induced by prompting and by finetuning are mediated by the same linear trait directions, so finetuning on data that implies a trait moves the model along the trait’s persona vector as a system prompt would; Chen et al. suspect personas are latent factors that persist across many tokens | Chen et al. (2025), LIT-1998, read in NOTE-1524. The mediating reading is the authors’ framing and PSM’s use of the paper (LIT-1952: training-time shifts “can be regarded as conditioning”). What the paper shows is correlation of shift with expression, and steering effects in both directions; that the regularizer against the shift fails, with the trait moving to other directions, counts against a single direction being the carrier. Proposed for that gap. | Proposed |
| THEORY-1335 | In Juarrero’s constraint account, context-independent constraints take conditions away from equiprobability and context-dependent ones away from independence (after Gatlin); enabling constraints couple separate processes into a coherent dynamic whose constitutive constraints then act top down as second-order governing constraints that confine its components to a subregion of state space; a constraint is defined as what raises or lowers barriers to energy flow without transferring kinetic energy, carries no time-scale condition, and the governing regime is held not to be other than the components | Juarrero (2023), LIT-1995, read in NOTE-1532 (Skimmed; chapters 2, 3, 6, 7, 11, 12, 15 and 16 in full). Active as a statement of what the account is: its kinds of constraint, its definition, and its top-down step, all stated in the text (pp. 25, 40, 67, 71, 79–84). It does not say that the account is true, that constraints transfer no energy, or that her constraint is the record’s (TERM-070’s). | Active |
| THEORY-1336 | In a cart-pole whose only given utility is 10-step empowerment, a controller that greedily picks the action leading to the more empowered successor balances the pole upright, though the states of highest empowerment lie off-centre and cannot be reached or sustained under the agent’s own dynamics; what the agent can keep is not where empowerment is highest | Klyubin, Polani and Nehaniv (2008), LIT-1951, pp. 4–7, read in NOTE-1514. A single simulation of one model with two actions, computed by the authors; the robustness of the off-centre maxima is stated, not shown. Proposed for want of a reproduction and a second system. | Proposed |
| THEORY-1337 | Neural field recordings carry aperiodic 1/f-like activity with power at every frequency, whose exponent varies with age, state and task; so power in a band, correlated power changes across bands, and ratios of band power can arise from the aperiodic component with no oscillation changing, and 1/f structure is a ubiquitous background of field data rather than a mark of any particular organization | Donoghue, Schaworonkow and Voytek (2021), LIT-1999, §§1 and 3, read in NOTE-1529. Active: the spectral argument is elementary (an aperiodic signal has power at all frequencies, and a change in its exponent moves every band), and the simulations and cited cases (the ADHD theta/beta ratio) are in the text. It does not say aperiodic activity is noise without physiological meaning; the paper calls it “a physiologically informative feature”. | Active |
| THEORY-1338 | In the Basic Psychological Need Satisfaction and Frustration Scale as Chen et al. built it, the distinction between satisfaction and frustration coincides with item direction: every satisfaction item states a positive experience and every frustration item an aversive one, so the better fit of six factors over three, which is the scale’s evidence that frustration is a separate dimension, is also what a keying or valence factor would produce | Chen et al. (2015), LIT-2000, read in NOTE-1527 from the publisher’s typeset copy in the ULB repository. Active as a statement about the instrument, checked against its Table 3 item by item and its model comparison (ΔSBSχ²(12) = 450.79, p. 226). It does not say the frustration dimension is an artefact, only that this evidence cannot tell it from one; that test is Murphy et al.’s (LIT-1978), unread. | Active |
| THEORY-1339 | In multi-turn conversations a chat model’s persona is not fixed for the episode: its position along the Assistant Axis is set mainly by the most recent user message (ridge R² 0.53–0.77 from message embeddings) rather than by where it was before (R² 0.10 for the change), so that therapy-like and AI-philosophy conversations drift away from the Assistant and coding and writing ones do not | Lu et al. (2026), LIT-1991, read in NOTE-1505. The figures are the paper’s (§§4.1–4.2), from 100 synthetic conversations per domain with frontier models playing the user. Proposed because the users are simulated, the conversations are generated by domain, and the regression is on embeddings of whole messages; the authors themselves ask for a human study. | Proposed |
| THEORY-1340 | Training forms a task-defined, low-dimensional subregion of prefrontal and premotor population activity (a preparatory subspace, an axis of choice organized as a line attractor) that constrains a monkey’s delayed response top down, holding behavior to what the task requires while the trial’s cue and evidence select within it; Juarrero’s reading of Churchland et al. 2012 and Mante, Sussillo et al. 2013 as governing constraints and as neural correlates of prior and proximate intentions | Juarrero (2023), LIT-1995, ch. 15 (pp. 223–232), read in NOTE-1532; the primary studies are not held. The subspaces and their predictive power are the studies’ findings as the chapter reports them. That the subspace controls behavior top down, is “the standing cause of the response” (p. 230) and correlates with prior and proximate intentions (pp. 229–231) is the book’s reading. Proposed for that step: the evidence reported is dimensionality reduction, prediction and a network simulation, with no intervention on the pattern. | Proposed |
| THEORY-1341 | In Jennings’s hybrid account, attention is prioritization of processing by a subject that is the whole collection of an organism’s fixed, formed and fluid interests, separated from filtering by whether selection answers to that collection, marked by feedback from dorsolateral prefrontal cortex; when interests are equally weighted, attention breaks the stalemate and updates the chosen option’s value, so that a fluid interest becomes a formed one | Jennings (2026), LIT-1963, §6, read in NOTE-1508. The operational half of the paper: what attention is, how it is told from filtering, and how it forms interests. The stalemate mechanism is taken from Voigt 2022 (LIT-1976), registered unread. Proposed because the criterion is inferred, not tested, and the paper reports no data. It does not say the subject is contextually emergent (THEORY-1314) or that attention is the source of a free will. | Proposed |
| THEORY-1342 | In Transformer attention the weights each query puts on the positions depend only on query–key compatibility, softmax(QKᵀ/√d_k), and the output is those weights applied to the values, so for a fixed input what a head selects and what it transports are separate factors; because queries, keys and values are all projections of the same input, the separation holds only with the input, and so the pattern, held fixed | Vaswani et al. (2017), LIT-1959, read in full in NOTE-1501, eq. 1 and §3.2.2; the circuit vocabulary is Elhage et al.’s (LIT-1534, THEORY-988). Active: it is the definition of the mechanism, checked against the equations. It does not say that heads are interpretable observers, which the paper supports only with visualizations, or that the separation survives composition across layers. | Active |
| THEORY-1343 | The first-order picture in which a small integral of motion Q of a many-body Hamiltonian is, under weak local noise, the slowest Lindbladian eigenoperator holds at large system size whenever its leak ε out of span{Q} satisfies ε ≲ γ ≪ 1, because the gap controlling the perturbation is not the exponentially small level spacing but one of order min(γL, √(v_Bγ)), set by the ballistic growth of the operators Q leaks into | Yang and Abanin (2025), LIT-1958, §IV, read in NOTE-1534. Proposed because the argument assumes fully chaotic operator growth for the complement, is checked numerically only at nine sites, and is qualified by the authors themselves: hydrodynamic modes give a continuum of slow modes in the Mori limit, so the gap “might not exist at all” outside sectors orthogonal to them. | Proposed |
| THEORY-1344 | Empowerment is the channel capacity from an agent’s next n actions to its sensor n steps later, an open-loop, interventional measure of how many perceptibly different futures the agent can bring about, which counts no control the agent cannot perceive; given side information about the channel’s state it is never lower, so it is ordered by what the agent can read, from full state through its own sensor history to none | Klyubin, Polani and Nehaniv (2005, 2008), LIT-1965 and LIT-1951, read in full in NOTE-1511 and NOTE-1514. Active as definitions and one inequality, re-derived. It does not say empowerment is what organisms maximize, which the authors offer as a hypothesis in a weak form only, nor that it prices control cost or viability. | Active |
| THEORY-1345 | In three cross-sectional studies of undergraduates, most of the variance in adult attachment security lay within persons, across relational partners (56–79%, error included), and relationship-specific satisfaction of the needs for autonomy, competence and relatedness predicted relationship-specific security in every relationship tested, also with the relatedness items removed; relatedness was the strongest unique predictor, then autonomy, then competence | La Guardia, Ryan, Couchman and Deci (2000), LIT-1979, read in NOTE-1523. Active as a statement of the associations the three studies report, with their sizes. It does not say that need satisfaction causes security, which the authors say their data cannot show and believe runs both ways (p. 381). | Active |
| THEORY-1346 | In rat cortical slices with synapses blocked, extracellular fields of the local field potential’s size, applied by an electrode, shift the membrane potential of layer 5 pyramidal neurons by less than 0.5 mV at frequencies up to 100 Hz and, with spiking driven by current, phase-lock spike times without changing spike counts, most effectively for slow fields, and synchronize nearby neurons; the authors explain the effect by Kirchhoff’s circuit laws and a fixed firing threshold | Anastassiou et al. (2011), LIT-1953, read in NOTE-1516 from the gwern.net scan at the owner’s direction. Active as a statement of what the experiments measured, which the paper reports with sizes, samples and corrected tests. It does not say that the fields neurons generate do this in vivo, that ephaptic coupling bears on attention or experience, or that it is evidence against micro-level description, which is the use Jennings makes of it (LIT-1963, p. 35). | Active |
| THEORY-1347 | In Patrick, Knee, Canevello and Lonsbary’s three correlational studies, perceiving that a romantic partner fulfils one’s needs for autonomy, competence and relatedness goes with better relationship quality, with relatedness the strongest unique predictor and the partner’s fulfilment adding to one’s own; but the measure does not separate the needs, its autonomy and competence subscales correlating .96 once corrected for unreliability | Patrick et al. (2007), LIT-1971, read in NOTE-1515 from the article on the SDT site. Active as a careful reading of reported results with their sizes and samples: eight pooled samples (N = 1,918), 66 couples, and 120 diarists with 908 disagreements, all self-report, mostly women students. It does not say need fulfilment causes relationship quality, that autonomous motivation mediates it (the mediation is cross-sectional), or that the three needs are distinct dimensions. | Active |
| THEORY-1348 | In Froese’s Irruption Theory an agent’s motivations make a difference to behaviour only as an increase in its material underdetermination, measurable at best indirectly as neural or behavioural entropy, and such irruptions are by the theory’s own terms undirected: scaled up by chaos, 1/f noise or criticality, they loosen the current organization but “cannot force the formation of the behavior that is to come”, so the theory places behaviour’s direction in the body’s attunement and not in the irruption | Froese (2023), LIT-1950, read in full in NOTE-1521 from PubMed Central’s copy. Active as a statement of what the theory says: its three axioms, its three theses, and the commitment that irruptions are undirected, all in the text (§§5.1–5.2.3). It does not say that the theory is true, that neural entropy measures motivation, or that attunement answers the luck objection (THEORY-1321, Proposed). | Active |
| THEORY-1349 | In two cross-lagged panel studies of university students, a negatively worded self-report of need frustration predicted later depressive symptoms (standardized β .13 to .18 over three lags) and later negative affect, net of earlier depression and negative affect, while negative affect did not predict later depression; depression also predicted later need frustration at one lag of two | Levine et al. (2021), LIT-1974, read in NOTE-1510 from the version of record in PMC. Active as a statement of the reported paths, checked against Tables 2, 4 and 5. It does not say the frustration causes the depression: the models are traditional cross-lagged panels without random intercepts, so their lagged paths mix stable between-person differences, the reverse path was as large as the forward one at the first lag, and every variable is a self-report. | Active |
| THEORY-1350 | The Persona Selection Model holds that pre-training gives a language model a distribution over personas, that post-training updates it into a posterior over Assistant personas which runtime context keeps conditioning, and that the Assistant’s traits are a key determiner of behaviour; it disowns a single coherent persona and exhaustiveness, and names as open a router that selects personas and could carry goals no persona has | Marks, Lindsey and Olah (2026), LIT-1952, read in full in NOTE-1512. Active as a statement of what the model says and does not say, all of it in the text. It does not say that the model is true: the authors are “overall unsure how complete” it is, its evidence is surveyed rather than new, and its updating is offered as “can be viewed as”, with the strict form said to be too strong. | Active |
| THEORY-1351 | In West, Fisher, Gardner and Kiers’s account, a transition in individuality is defined by two separable conditions, mutual dependence (parts that once replicated alone can replicate only within the larger unit) and negligible within-group conflict, and proceeds by forming a cooperative group and then transforming it, with no clear border between the steps; across transitions what explains them is an ecological benefit to cooperation together with group formation that unites the members’ interests (clonal bottlenecks, lifetime monogamy, vertical transmission of clonal symbionts), while kin discrimination and the repression of competition played relatively minor roles | West et al. (2015), LIT-2003, read in NOTE-1538. A colloquium review: the definition and the two steps are the authors’ framework, and the explanatory claim is drawn from the comparative literature they cite. Proposed because they call it “tentative”, and because the theory for transitions between species is missing on their own account. It differs from THEORY-141 on mechanism: group formation, not policing, does the work. | Proposed |
| THEORY-1352 | In Van Lange and Bergmann’s model, human cooperation is readily sustained between individuals, above all in dyads, through precise reciprocity, empathy and a partner who cannot be excluded at no cost, and is fragile between groups: categorization alone yields mistrust and in-group favouritism by bounded reciprocity, observed out-group favouritism hardens it into distrust, and only negative interdependence, real or perceived, turns that into costly competition, aggression and hate, so that the processes that build in-group cooperation can fuel intergroup conflict | Van Lange and Bergmann (2026), LIT-2002, read in NOTE-1537. A Perspective: a staged model drawn from the authors’ selection of the literature on social dilemmas and intergroup relations, with no new data and no pooled effect sizes. Proposed because the stages are proposed and not tested together. The refinement that matters to the record: lower cooperation between groups does not need conflicting interests, and harm to the out-group does. | Proposed |